Department of Mathematics, Fall_2022
https://services.math.duke.edu/mcal?listgroup-0
Department of Mathematics Upcoming Seminarsen-us2024-03-29T11:56:49-04:00https://services.math.duke.edu/mcal2024-01-01T12:00:00-05:002dailyMath Teaching Professional Development
https://services.math.duke.edu/mcal?abstract-12136
For new graduate students: Math GTA support and development, overview of Duke Math's calculus courses, role of graduate assistants, how labs work, evaluating student work, practice lab presentation assignments, Q&A. Lunch included.Shira Viel, Tori Akin, Sarah Schott (Duke University, Math)2022-08-22T11:15:00-04:0012136Professional developmentTraining WeekMonday, August 22, 2022, 11:15amMon, 22 Aug 2022 11:15:00 EDTPhysics 235Mon, 22 Aug 2022 14:15:00 EDTFall, 2022Handling Office Hours
https://services.math.duke.edu/mcal?abstract-12138
For first time graduate student instructors and new faculty.<a href="mailto:cbray@math.duke.edu">Clark Bray</a> (Duke University, Math)2022-08-24T10:00:00-04:0012138Professional developmentTraining WeekWed, 24 Aug 2022 12:00:00 EDTFall, 2022Wednesday, August 24, 2022, 10:00amWed, 24 Aug 2022 10:00:00 EDTPhysics 119Diversity, Equity and Inclusion in the classroom
https://services.math.duke.edu/mcal?abstract-12140
For first time graduate instructors, new graduate students and new faculty.Shira Viel, Tori Akin (Duke University, Math)2022-08-24T13:00:00-04:0012140Professional developmentTraining WeekFall, 2022Wed, 24 Aug 2022 14:00:00 EDTPhysics 235Wed, 24 Aug 2022 13:00:00 EDTWednesday, August 24, 2022, 1:00pmIntroduction to Duke Libraries
https://services.math.duke.edu/mcal?abstract-12142
For new graduate students and faculty.Ciara Healy (Duke University, Libraries)2022-08-24T14:45:00-04:0012142Professional developmentTraining WeekWednesday, August 24, 2022, 2:45pmPhysics 119Wed, 24 Aug 2022 14:45:00 EDTWed, 24 Aug 2022 15:45:00 EDTFall, 2022History of Lab Calculus at Duke
https://services.math.duke.edu/mcal?abstract-12144
For new graduate students: the history and philosophy of Calculus in Duke Math.<a href="mailto:bookman@math.duke.edu">Jack Bookman</a> (Duke University, Math)2022-08-25T13:00:00-04:0012144Professional developmentTraining WeekThursday, August 25, 2022, 1:00pmPhysics 119Thu, 25 Aug 2022 13:00:00 EDTIntFall, 2022Thu, 25 Aug 2022 14:00:00 EDTTeaching information for new and visiting faculty
https://services.math.duke.edu/mcal?abstract-12146
For new and visiting faculty: the Chair and Supervisor of First Year Instruction provide teaching information.<a href="mailto:cbray@math.duke.edu">Robert Bryant, Clark Bray</a> (Duke University, Math)2022-08-26T10:30:00-04:0012146Professional developmentTraining WeekFall, 2022Fri, 26 Aug 2022 12:30:00 EDTFriday, August 26, 2022, 10:30amFri, 26 Aug 2022 10:30:00 EDTPhysics 119Grading exams
https://services.math.duke.edu/mcal?abstract-12148
For new graduate students, new faculty, and first time graduate instructors: discussion of grading student midterms and final exams; goals, preconceptions, strategies. Gradescope.<a href="mailto:cbray@math.duke.edu">Clark Bray</a> (Duke University, Math)2022-08-26T13:00:00-04:0012148Professional developmentTraining WeekFall, 2022Fri, 26 Aug 2022 14:30:00 EDTPhysics 130Fri, 26 Aug 2022 13:00:00 EDTFriday, August 26, 2022, 1:00pmSakai and Duke Hub
https://services.math.duke.edu/mcal?abstract-12149
For first time graduate instructors and new faculty: Introduction to Sakai and Duke Hub. Have your Duke NetID and bring your laptop.<a href="mailto:cbray@math.duke.edu">Clark Bray</a> (Duke University, Math)2022-08-26T15:00:00-04:0012149Professional developmentTraining WeekPhysics 119Fri, 26 Aug 2022 15:00:00 EDTFriday, August 26, 2022, 3:00pmFri, 26 Aug 2022 16:00:00 EDTFall, 2022Math Placement Open House
https://services.math.duke.edu/mcal?abstract-12151
For first year undergrads: information session about placement in math courses.Clark Bray, Sarah Schott, Shira Viel, Rann Bar-On, Hugh Bray (Duke University, Math)2022-08-27T09:00:00-04:0012151Professional developmentTraining WeekSat, 27 Aug 2022 12:00:00 EDTFall, 2022Saturday, August 27, 2022, 9:00am123 PhysicsSat, 27 Aug 2022 09:00:00 EDTMath TA orientation
https://services.math.duke.edu/mcal?abstract-12154
For all Math TAs: expectations, role, facilitating group work, essentials of tutoring. Includes dinner for TAs and instructors.<a href="mailto:kristen@math.duke.edu">Kristen Gerondelis</a> (Duke University, Math)2022-08-28T16:00:00-04:0012154Professional developmentTraining WeekFall, 2022IntSun, 28 Aug 2022 18:00:00 EDTSun, 28 Aug 2022 16:00:00 EDTPhysics 128Sunday, August 28, 2022, 4:00pmMulticontinuum homogenization and applications
https://services.math.duke.edu/mcal?abstract-12170
In this talk, we will start with some main concepts in multiscale modeling and temporal splitting. Our goal is to model processes in multiscale media without scale separation and with high contrast. We assume that the coarse grid doesn’t resolve the scales and the contrast. To deal with these problems, I will introduce multiscale methods that use multicontinua approaches. These approaches use additional macroscopic variables. I will discuss the convergence of these approaches and show that these methods converge independent of the contrast. The multicontinua approaches can benefit from machine learning techniques, which I will discuss. I will also consider how multiscale methods can be used for temporal splitting. High contrast brings stiffness to the system, which requires small time steps. We will introduce partial explicit methods that construct time discretizations with the time stepping that is independent of the contrast. Numerical results will be shown to back up our theories. We will discuss how these approaches are used in machine learning.Yalchin Efendiev (Texas A&M University, Mathematics)2022-08-30T15:15:00-04:0012170applied math and analysisApplied Math And Analysis SeminarFall, 2022Tue, 30 Aug 2022 16:15:00 EDTTuesday, August 30, 2022, 3:15pmTue, 30 Aug 2022 15:15:00 EDTPhysics 119Mean-Field Games for Scalable Computation and Diverse Applications
https://services.math.duke.edu/mcal?abstract-12187
Mean field games (MFGs) study strategic decision-making in large populations where individual players interact via specific mean-field quantities. They have recently gained enormous popularity as powerful research tools with vast applications. For example, the Nash equilibrium of MFGs forms a pair of PDEs, which connects and extends variational optimal transport problems. This talk will present recent progress in this direction, focusing on computational MFG and engineering applications in robotics path planning, pandemics control, and Bayesian/AI sampling algorithms. This is based on joint work with the MURI team led by Stanley Osher (UCLA).<a href="mailto:WUCHEN@mailbox.sc.edu">Wuchen Li</a> (University of South Carolina, Mathematics)2022-09-06T15:15:00-04:0012187applied math and analysisApplied Math And Analysis SeminarPhysics 119Tue, 06 Sep 2022 15:15:00 EDTTuesday, September 6, 2022, 3:15pmYesFall, 2022Tue, 06 Sep 2022 16:15:00 EDTIntroduction to Hodge Theory 1
https://services.math.duke.edu/mcal?abstract-12183
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
<p>
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
<br>
https://Sakai.duke.edu/portal/site/htom
</p><a href="https://scholars.duke.edu/person/jin.lee">Jin Lee</a> (Duke U, Mathematics)2022-09-07T11:30:00-04:0012183Department of MathematicsHodge TheoryLearning Seminar on Hodge Theory & O-MinimalityWednesday, September 7, 2022, 11:30amWed, 07 Sep 2022 11:30:00 EDTGross 304BFall, 2022Wed, 07 Sep 2022 13:00:00 EDTControl-Theoretic Models of Environmental Crime
https://services.math.duke.edu/mcal?abstract-12176
We present two models of perpetrators' decision-making in extracting resources from a protected area. It is assumed that the authorities conduct surveillance to counter the extraction activities, and that perpetrators choose their post-extraction paths to balance the time/hardship of travel against the expected losses from a possible detection. In our first model, the authorities are assumed to use ground patrols and the protected resources are confiscated as soon as the extractor is observed with them. The perpetrators' path-planning is modeled using the optimal control of randomly-terminated process. In our second model, the authorities use aerial patrols, with the apprehension of perpetrators and confiscation of resources delayed until their exit from the protected area. In this case the path-planning is based on multi-objective dynamic programming. Our efficient numerical methods are illustrated on several examples with complicated
geometry and terrain of protected areas, non-uniform distribution of protected resources, and spatially non-uniform detection rates due to aerial or ground patrols.<a href="https://math.uchicago.edu/~ecartee/">Elliot Cartee</a> (University of Chicago, Mathematics)2022-09-09T12:00:00-04:0012176mathematical biologyapplied math and analysisMathematical Biology SeminarFri, 09 Sep 2022 13:00:00 EDTFall, 2022Yeshttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/12175.png" /></div>
Friday, September 9, 2022, 12:00pmFri, 09 Sep 2022 12:00:00 EDTPhysics 119Spherical Topicalization and Berkovich Analytification
https://services.math.duke.edu/mcal?abstract-12105
Tropicalization is the process by which algebraic varieties are assigned a "combinatorial shadow". I will review the notion of tropicalization of a toric variety and recent work on extending this to spherical varieties. I will then present how one can construct a deformation retraction from the Berkovich analytification of a spherical variety to its tropicalization.<a href="https://web.ma.utexas.edu/users/coles/">Desmond Coles</a> (University of Texas--Austin, Mathematics)2022-09-09T15:00:00-04:0012105algebraic geometryAlgebraic Geometry SeminarFall, 2022YesFri, 09 Sep 2022 16:00:00 EDTFri, 09 Sep 2022 15:00:00 EDTGross 304BFriday, September 9, 2022, 3:00pmOn the Landau Equation
https://services.math.duke.edu/mcal?abstract-12226
The Landau equation is a well known model in kinetic theory representing the evolution of the density particles with certain velocities in a plasma. It is a scalar, nonlinear, parabolic equation. The global well posedness of the initial value problem is a major open problem in the area. We discuss some ideas and difficulties concerning this equation.Luis Silvestre (University of Chicago)2022-09-12T09:00:00-04:0012226Department of MathematicsSpecial Analysis SeminarMon, 12 Sep 2022 10:00:00 EDTFall, 2022Mon, 12 Sep 2022 09:00:00 EDT150 PhysicsMonday, September 12, 2022, 9:00amComparison geometry and spacetime harmonic functions
https://services.math.duke.edu/mcal?abstract-12181
Comparison theorems are the basis for our geometric understanding of Riemannian manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson torus band inequality, which bounds the distance between the two sides of a Riemannian torus-cross-interval with positive scalar curvature by a sharp constant. We will give a new qualitative version of this and similar band-type inequalities in dimension 3 using the notion of spacetime harmonic functions, which recently played the lead role in our new proof of the positive mass theorem. Other applications include new versions of Bonnet-Myer's diameter estimate and Llarull's theorem which do not require a completeness assumption. This is joint work with Sven Hirsch, Marcus Khuri, and Yiyue Zhang.<a href="mailto:demetre.kazaras@duke.edu">Demetre Kazaras</a> (Duke University)2022-09-12T15:15:00-04:0012181geometry/topologyGeometry/topology SeminarPhysics 119Mon, 12 Sep 2022 15:15:00 EDTMonday, September 12, 2022, 3:15pmMon, 12 Sep 2022 16:15:00 EDTFall, 2022Holder continuity up to the boundary for kinetic equations
https://services.math.duke.edu/mcal?abstract-12228
We consider a kinetic Fokker-Planck equation with rough coefficients and the spatial variable restricted to a bounded domain. There are recent results concerning interior Holder estimates for this class of equations following techniques by De Giorgi, Nash and Moser. In this talk, we discuss the regularity of the solutions on the boundary.Luis Silvestre (U. Chicago)2022-09-13T15:15:00-04:0012228applied math and analysisApplied Math And Analysis SeminarTue, 13 Sep 2022 16:15:00 EDTFall, 2022Tuesday, September 13, 2022, 3:15pmPhysics 119Tue, 13 Sep 2022 15:15:00 EDTIntroduction to Hodge Theory 2 & Introduction to O-Minimality 1
https://services.math.duke.edu/mcal?abstract-12220
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
<p>
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
<br>
https://Sakai.duke.edu/portal/site/htom
</p><a href="https://scholars.duke.edu/person/jin.lee">Jin Lee & Chongyao Chen</a> (Duke U, Mathematics)2022-09-14T11:30:00-04:0012220Department of MathematicsHodge TheoryLearning Seminar on Hodge Theory & O-MinimalityWednesday, September 14, 2022, 11:30amGross 304BWed, 14 Sep 2022 11:30:00 EDTWed, 14 Sep 2022 13:00:00 EDTFall, 2022Anomalous diffusion of microparticles in biological fluids
https://services.math.duke.edu/mcal?abstract-12201
The range of observed movement of individual microparticles (viruses, bacteria, organelles, etc) in biological fluids (mucus, cytoplasm, and interstitial fluid) poses a host of mathematical and statistical challenges. In contrast to the assumptions defining Brownian motion, which is the default model for random particle movement in viscous fluids, experimental data has revealed significant memory effects, persistent state-switching, and irregular geometric constraints. After taking a brief look at "what's out there in the data," we will focus on one model, the generalized Langevin equation, and an interesting associated appearance of infinite-dimensional dynamics.<a href="http://randommath.net">Scott McKinley</a> (Tulane University, Mathematics)2022-09-16T12:00:00-04:0012201mathematical biologyMathematical Biology SeminarFri, 16 Sep 2022 12:00:00 EDTPhysics 119Friday, September 16, 2022, 12:00pmhttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/12200.jpg" /></div>
Fall, 2022Fri, 16 Sep 2022 13:00:00 EDTLogarithmic Gromov-Witten Invariants under Degeneration
https://services.math.duke.edu/mcal?abstract-12082
Tropical geometry has been an important and powerful tool in enumerative geometry. One can view logarithmic geometry as a hidden bridge between the tropical world and the algebraic world. In this talk, I will introduce the theory of logarithmic Gromov-Witten invariants. I will present the decomposition theorem of Abramovich-Chen-Gross-Siebert under log smooth degenerations. I will show how we use the perturbation of tropical curves to obtain a splitting formula of log Gromov-Witten invariants, with the assumption of the gluing strata being toric varieties.<a href="https://web.ma.utexas.edu/users/yixianwu/">Yixian Wu</a> (University of Miami, Institute of the Mathematical Sciences of the Americas)2022-09-16T15:00:00-04:0012082algebraic geometryAlgebraic Geometry SeminarFri, 16 Sep 2022 16:00:00 EDTIntFall, 2022Friday, September 16, 2022, 3:00pmFri, 16 Sep 2022 15:00:00 EDTGross 304BNahm transforms and ALF Spaces
https://services.math.duke.edu/mcal?abstract-12172
In this talk we consider the moduli space of Yang-Mills instantons on the family of hyperkahler 4 manifolds known as multi-center TaubNUT spaces.
We describe the Nahm transform for flat manifolds. Then we sketch its extension to the above hyperkahler family, where it defines an isometry between the moduli space of instantons on the multi-center TaubNUT and the moduli space of solutions of a rococo system of ordinary differential equations.
This is joint work with Sergey Cherkis and Andres Larrain Hubach<a href="mailto:stern@math.duke.edu">Mark Stern</a> (Duke, Mathematics)2022-09-19T15:15:00-04:0012172geometry/topologyGeometry/topology SeminarMonday, September 19, 2022, 3:15pmPhysics 119Mon, 19 Sep 2022 15:15:00 EDTMon, 19 Sep 2022 16:15:00 EDTFall, 2022YesData-driven Robust Hypothesis Testing via Wasserstein Uncertainty Sets
https://services.math.duke.edu/mcal?abstract-12211
We consider a data-driven robust hypothesis testing problem where the true data-generating distributions are unknown and indirectly observable through limited training samples. We first construct the distributional uncertainty sets that contain distributions within a certain Wasserstein distance from a nominal distribution estimated from the training samples. The learning task is to solve the optimal test that minimizes the worst-case error within the uncertainty sets. By exploiting the geometry of the Wasserstein distance, we show that this problem can be solved efficiently through a tractable linear program reformulation. We also construct a confidence region for the optimal oracle test and present the generalization bound. The proposed robust test has great potential in many other problems and applications such as health care, anomaly detection, classification, etc.Liyan Xie (Chinese University of Hong Kong, Shenzhen)2022-09-20T15:15:00-04:0012211applied math and analysisApplied Math And Analysis SeminarFall, 2022Tue, 20 Sep 2022 16:15:00 EDTTuesday, September 20, 2022, 3:15pmPhysics 119Tue, 20 Sep 2022 15:15:00 EDTIntroduction to o-minimality, 2
https://services.math.duke.edu/mcal?abstract-12222
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
<p>
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
<br>
https://Sakai.duke.edu/portal/site/htom
</p><a href="https://scholars.duke.edu/person/chongyao.chen">Chongyao Chen</a> (Duke U, Mathematics)2022-09-21T11:40:00-04:0012222Department of MathematicsHodge TheoryLearning Seminar on Hodge Theory & O-MinimalityFall, 2022Wed, 21 Sep 2022 13:00:00 EDTWednesday, September 21, 2022, 11:40amWed, 21 Sep 2022 11:40:00 EDTGross 304BRegular quotients and Hitchin fibrations (joint work with Ngô B.-C.)
https://services.math.duke.edu/mcal?abstract-12203
Orbital integrals for the Lie algebra can be analyzed using the Hitchin fibration. In turn the Hitchin fibration can be analyzed via the morphism g^{reg} ----> g//G from the regular elements of the Lie algebra, to the GIT quotient by the adjoint action. In trying to generalize this story by replacing the action of G on g by the action of G on some sufficiently nice variety M, we must replace the GIT quotient with what we call the regular quotient. This talk will look at the reasons for this, and the difference between the GIT and regular quotients in the case of G acting on G by conjugation (when the derived group of G is not simply connected), G acting on the commuting scheme, and G acting on the Vinberg monoid.<a href="mailto:bmor@uchicago.edu">Benedict Morrissey</a> (University of Chicago, Mathematics)2022-09-21T15:15:00-04:0012203Number TheoryNumber Theory SeminarWednesday, September 21, 2022, 3:15pmPhysics 119Wed, 21 Sep 2022 15:15:00 EDTYesFall, 2022Wed, 21 Sep 2022 16:15:00 EDTMechanisms Underlying Spatiotemporal Patterning in Microbial Collectives: A Mathematical Perspective
https://services.math.duke.edu/mcal?abstract-12199
We describe a spatial Moran model that captures mechanical interactions and directional growth in spatially extended populations. The model is analytically tractable and completely solvable under a mean-field approximation and can elucidate the mechanisms that drive the formation of population-level patterns. As an example, we model a population of E. coli growing in a rectangular microfluidic trap. We show that spatial patterns can arise because of a tug-of-war between boundary effects and growth rate modulations due to cell-cell interactions. We will then discuss how our model reveals that changes to a cell-shape describing parameter may manifest at the population level of the microbial collective. Specifically, we discuss mechanisms revealed by our model on how we may be able to control spatiotemporal patterning by modifying cell shape of a given strain in a multi-strain microbial consortium.<a href="https://www.math.fsu.edu/~karamche/">Bhargav Karamched</a> (Florida State University, Mathematics)2022-09-23T12:00:00-04:0012199mathematical biologyMathematical Biology Seminarhttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/12198.jpg" /></div>
Fri, 23 Sep 2022 13:00:00 EDTFall, 2022Fri, 23 Sep 2022 12:00:00 EDTPhysics 119Friday, September 23, 2022, 12:00pmProper Period Matrix Representations at Infinity
https://services.math.duke.edu/mcal?abstract-12244
An important problem in Hodge theory and its application to the study of moduli is to generalize the Satake-Baily-Borel compactification and Borel’s extension theorem to arbitrary period mappings. I will outline some of the difficulties that arise, and explain how the problem can be reduced to an extension problem (a la Ohsawa-Takegoshi, but without the need for bounds on the L2 norms).
If you wish to join by Zoom, please contact Haohua Deng [haohua.deng@duke.edu] who has generously agreed to facilitate remote attendance.<a href="https://services.math.duke.edu/~robles/index.html">Colleen Robles</a> (Duke, Mathematics)2022-09-23T15:00:00-04:0012244algebraic geometryAlgebraic Geometry SeminarFall, 2022Fri, 23 Sep 2022 16:00:00 EDTGross 304BFri, 23 Sep 2022 15:00:00 EDTFriday, September 23, 2022, 3:00pmSpecial Lagrangians from the perspective of Morse theory
https://services.math.duke.edu/mcal?abstract-12158
In this talk, we consider a Lagrange multipliers problem where the constraint is a section
of a bundle $E \rightarrow M$. We relate the Morse homology of a function restricted to $s^{-1}(0)$ to the Morse homology of the associated Lagrange function on the total space $E^{*}$. We then discuss a similar (infinite- dimensional) Lagrange multipliers problem that first appeared in Donaldson and Segal’s paper Gauge Theory in Higher Dimensions II. The long term goal is to apply Floer theory to a functional whose critical points are generalizations of three-dimensional, special Lagrangian submanifolds. We describe the relevant functionals, critical points, and gradient trajectories.<a href="mailto:ewindes@u.rochester.edu">Emily Windes</a> (University of Rochester, Mathematics)2022-09-26T15:15:00-04:0012158geometry/topologyGeometry/topology SeminarMon, 26 Sep 2022 15:15:00 EDTPhysics 119Monday, September 26, 2022, 3:15pmMon, 26 Sep 2022 16:15:00 EDTFall, 2022Introduction to o-minimality, 3
https://services.math.duke.edu/mcal?abstract-12260
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
<p>
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
<br>
https://Sakai.duke.edu/portal/site/htom
</p><a href="https://scholars.duke.edu/person/chongyao.chen">Chongyao Chen</a> (Duke U, Mathematics)2022-09-28T11:45:00-04:0012260Department of MathematicsHodge TheoryLearning Seminar on Hodge Theory & O-MinimalityFall, 2022Wed, 28 Sep 2022 13:00:00 EDTWednesday, September 28, 2022, 11:45amGross 304BWed, 28 Sep 2022 11:45:00 EDTDMI/MEMS Seminar
https://services.math.duke.edu/mcal?abstract-12217
Abstract:
Designing optical metamaterials from colloidal nanocrystal assemblies
Colloidal noble metal nanocrystals (NCs) have metal cores and organic or inorganic ligand shells and are known for their size- and shape-dependent localized surface plasmon resonances. In this talk, I will describe the use of these NCs as building blocks of assemblies with designer optical properties for 2D and 3D metamaterials. Chemical exchange of the long ligands used in NC synthesis with more compact ligand chemistries reduces the interparticle distance (d) and increases interparticle coupling. This ligand-controlled coupling allows us to tune through a dielectric-to-metal phase transition, seen by a 1010 range in DC conductivity and a dielectric permittivity ranging from everywhere positive to everywhere negative across the whole range of optical frequencies, and design assemblies that are strong optical absorbers or scatterers. We harness the solution-processability and physical properties of colloidal NCs to pattern NC superstructures for large-area metamaterials, demonstrating 2D extreme bandwidth quarter-wave plates and optical sensors. By exploiting the different chemical and physical properties of NC assemblies from bulk thin films, we construct NC/bulk bilayer heterostructures, that upon ligand exchange fold into 3D structures providing a simple route to 3D metamaterials. We exploit these folded, bilayer heterostructures to demonstrate chiral structures that form broadband circular polarizers. Time permitting, I will expand on these ideas to include other NC compositions and their use to create stimuli-responsive 2D and 3D optical metamaterialsCherie R. Kagan (University of Pennsylvania)2022-09-28T12:00:00-04:0012217Other Meetings and EventsWed, 28 Sep 2022 13:00:00 EDTFall, 2022Wed, 28 Sep 2022 12:00:00 EDTNoneWednesday, September 28, 2022, 12:00pmThe Kloosterman circle method and weighted representation numbers of positive definite quadratic forms
https://services.math.duke.edu/mcal?abstract-12168
We develop a version of the Kloosterman circle method with a bump function that is used to provide asymptotics for weighted representation numbers of positive definite integral quadratic forms. Unlike many applications of the Kloosterman circle method, we explicitly state some constants in the error terms that depend on the quadratic form. This version of the Kloosterman circle method uses Gauss sums, Kloosterman sums, Salié sums, and a principle of nonstationary phase. If time permits, we may discuss a potential application of this version of the Kloosterman circle method to a proof of a strong asymptotic local-global principle for certain Kleinian sphere packings.<a href="https://scholars.duke.edu/person/Edna.Jones">Edna Jones</a> (Duke University)2022-09-28T15:15:00-04:0012168Number TheoryNumber Theory SeminarFall, 2022YesWed, 28 Sep 2022 16:15:00 EDTPhysics 119Wed, 28 Sep 2022 15:15:00 EDTWednesday, September 28, 2022, 3:15pmMath Art and Snacks
https://services.math.duke.edu/mcal?abstract-12223
Brainstorm Math Art to decorate Gross Hall 3rd Floor/Math grad student office areas. Please bring a proposal or an art project. Preferably not a poster.Ingrid Daubechies 2022-09-28T16:30:00-04:0012223Other Meetings and EventsOther Meetings And Events SeminarWed, 28 Sep 2022 17:30:00 EDTFall, 2022Wednesday, September 28, 2022, 4:30pmWed, 28 Sep 2022 16:30:00 EDTGross Hall 355Hypocoercivity for Langevin dynamics
https://services.math.duke.edu/mcal?abstract-12272
This will be the last in his sequence of an introductory lecture on Hypocoercivity for Langevin dynamics. For those who have not attended the previous lectures and are familiar with Langevin dynamics, the talk should be accessible.
We will continue our discussion on convergence to equilibrium for second-order Langevin dynamics using the Poincare approach. We'll recap convergence in H^1(\mu) and then we'll talk about the direct L^2(\mu) method of Dolbeault, Mouhot, and Schmeiser, also called the DMS approach.<a href="mailto:dherzog@iastate.edu">David Herzog</a> (Iowa State)2022-09-29T15:15:00-04:0012272probabilityProbability SeminarPhysics 119Thu, 29 Sep 2022 15:15:00 EDTThursday, September 29, 2022, 3:15pmFall, 2022YesThu, 29 Sep 2022 16:15:00 EDTRTG22SiFINeT: A clustering-independent method to identify cell-type-specific feature genes and annotate cells
https://services.math.duke.edu/mcal?abstract-12232
Single-cell sequencing has provided a means of quantifying cellular omic phenotypes. Identifying cell-type-specific feature genes is a crucial aspect of understanding cellular heterogeneity. Over the past decade, many methods have been developed to identify feature genes; however, these methods either depend on dubious clustering results or fail to annotate cell types with the identified feature genes. We develop a novel clustering-independent method, SiFINeT, to utilize the gene co-expression network topology to identify cell-type-specific feature genes. The identified genes can be used to calculate cellular feature scores and annotate cells with discrete cell types or continuous trajectories. SiFINet outperforms state-of-the-art methods in both feature gene identification and cell-type annotation. SiFINeT has successfully identified new markers in many studies, including new feature genes for senescent cells.<a href="https://sites.duke.edu/jichunxie/">Jichun Xi</a> (Duke University, Biostatistics and Mathematics)2022-09-30T12:00:00-04:0012232mathematical biologyMathematical Biology SeminarFri, 30 Sep 2022 13:00:00 EDTFall, 2022https://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/12231.jpg" /></div>
Friday, September 30, 2022, 12:00pmPhysics 119Fri, 30 Sep 2022 12:00:00 EDTEvery knot with unknotting number \leq 21 bounds a disc in a punctured K3 surface
https://services.math.duke.edu/mcal?abstract-12133
A question in knot theory that has become very popular recently is to classify what knots bound smooth discs in X - int(B^4), where X is a given closed 4-manifold. If X is a K3 surface, we show that every knot that can be unknotted with at most 21 crossing changes bounds a smooth disc in X - int(B^4). Our proof is constructive and based on the existence of a plumbing tree of 22 spheres in K3. We also prove a more general result when X is an elliptic surface E(n). This is joint work with Stefan Mihajlović.<a href="https://users.renyi.hu/~marengon/">Marco Marengon</a> (Alfred Renyi Institute of Mathematics)2022-10-03T15:15:00-04:0012133geometry/topologyGeometry/topology SeminarMon, 03 Oct 2022 16:15:00 EDTFall, 2022Monday, October 3, 2022, 3:15pmPhysics 119Mon, 03 Oct 2022 15:15:00 EDTRecent results on nodal sets for the Laplacian
https://services.math.duke.edu/mcal?abstract-12209
In the first half of the talk, we will discuss some recent work on characterizing the number of nodal sets for an eigenfunction that was initiated with Graham Cox and Chris Jones, which has been further developed with Greg Berkolaiko, Yaiza Canzani and Graham Cox. This work gives an especially nice means of quantifying the number of nodal sets of an eigenfunction and the importance of a so-called two-sided Dirichlet-to-Neumann map in our analysis (this also has a graph analog and can be informative for analyzing equipartitions of a given domain). Then, in the second half of the talk, we will use these results as motivation to discuss more closely properties of nodal sets for low energy eigenfunctions on nearly rectangular domains that we looked at in joint work with Tom Beck, Yaiza Canzani and Marichi Gupta.Jeremy Louis Marzuola (UNC Chapel Hill)2022-10-04T15:15:00-04:0012209applied math and analysisApplied Math And Analysis SeminarTuesday, October 4, 2022, 3:15pmPhysics 119Tue, 04 Oct 2022 15:15:00 EDTTue, 04 Oct 2022 16:15:00 EDTFall, 2022Definable Analytic Spaces, 1
https://services.math.duke.edu/mcal?abstract-12278
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
https://Sakai.duke.edu/portal/site/htom<a href="mailto:haohua.deng@duke.edu">Chongyao Chen/Haohua Deng</a> (Duke University)2022-10-05T11:45:00-04:0012278Hodge TheoryLearning Seminar on Hodge Theory & O-MinimalityWed, 05 Oct 2022 13:00:00 EDTFall, 2022Gross 304BWed, 05 Oct 2022 11:45:00 EDTWednesday, October 5, 2022, 11:45amSpatial ergodicity and quantitative central limit theorems for the stochastic heat equation
https://services.math.duke.edu/mcal?abstract-12241
In this lecture we will present some results on the asymptotic behavior of spatial averages over large blocks of the stochastic heat equation driven by a Gaussian noise which is white in time and it has an homogeneous spatial covariance. We will discuss the spatial ergodicity, that can be established using Poincaré’s inequality and quantitative central limit theorems for spatial averages. The goal is to show a rate of convergence in total variation distance, by means of a combination of Malliavin calculus techniques and Stein’s method for normal approximations.<a href="mailto:nualart@ku.edu">David Nualart</a> 2022-10-06T15:15:00-04:0012241probabilityProbability SeminarFall, 2022Thu, 06 Oct 2022 16:15:00 EDTThu, 06 Oct 2022 15:15:00 EDTZoom linkThursday, October 6, 2022, 3:15pmRiemannian optimization with three metrics for Hermitian PSD fixed rank constraints
https://services.math.duke.edu/mcal?abstract-12159
Hermitian PSD fixed rank constraint is used in many applications, e.g., it is also used for approximating the Hermitian PSD constraint. We study and compare three methodologies for minimizing f(X) with X being a Hermitian PSD fixed rank matrix. The first approach is the simplest factor-based Burer-Monteiro method, in which a PSD fixed rank matrix X is replaced by its low-rank decomposition YY^* thus an unconstrained minimization of f(YY^*) can be solved instead. The second approach is to regard the set of Hermitian PSD fixed rank matrices as an embedded manifold in the Euclidean space and consider the Riemannian optimization over the embedded manifold. The third approach is to regard it as a quotient manifold and consider the Riemannian optimization over the quotient manifold. For simplicity, we only consider the nonlinear conjugate gradient (CG) algorithm, which is an efficient algorithm in these methods. We show that CG in the first two methodolgies are equivalent to CG on the quotient manifold with suitably chosen metrics, retractions, and vector transports. We also analyze the condition number of the Riemannian Hessian under these different metrics. The difference in the condition number of the Riemannian Hessian under different metrics is consistent with the difference in the numerical performance of three methodologies for problems including matrix completion, phase retrieval, and interferometry recovery.Xiangxiong Zhang (Purdue)2022-10-11T15:15:00-04:0012159applied math and analysisApplied Math And Analysis SeminarTuesday, October 11, 2022, 3:15pmPhysics 119Tue, 11 Oct 2022 15:15:00 EDTFall, 2022Tue, 11 Oct 2022 16:15:00 EDTDefinible Analytic Spaces, 2
https://services.math.duke.edu/mcal?abstract-12282
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
https://Sakai.duke.edu/portal/site/htom<a href="https://www.hao-jia-umn-math.com/">Haohua Deng</a> (Duke University)2022-10-12T11:45:00-04:0012282Hodge TheoryLearning Seminar on Hodge Theory & O-MinimalityWed, 12 Oct 2022 13:00:00 EDTFall, 2022Wednesday, October 12, 2022, 11:45amGross 304BWed, 12 Oct 2022 11:45:00 EDTTime scale separation in life-long ovarian follicles population dynamics model
https://services.math.duke.edu/mcal?abstract-12262
In this talk, we will detail population dynamics approach to study the aging of the ovarian follicle
population. We revisit compartmental population dynamics model for ovarian follicles development [1] by
adding follicles interaction that result (directly or indirectly) from the control exerted onto their growth
and death rates by reproductive hormones. The shape of the follicle population distribution through time
is obtained thanks to a time scale difference between follicle activation and follicle growth [2]. We obtain
rigorously a limit model [3] that enable to study the effect of the growing follicle pool onto the quiescent
one. Finally, we show how to calibrate such compartmental models on mice using published population
count data and several perturbation scenarios [4].
References
[1] M. Faddy, E. Jones, and R. Edwards, An analytical model for ovarian follicle dynamics, J. Exp. Zool.,
197:173–185, 1976.
[2] C. Bonnet, K. Chahour, F. Clément, M. Postel, and R. Yvinec, Multiscale population dynamics in
reproductive biology : Singular perturbation reduction in deterministic and stochastic models, ESAIM
Proc. Surveys, 67:72–99, 2020.
[3] G. Ballif, F. Clément and R. Yvinec, Averaging of a Stochastic Slow-Fast Model for Population Dy-
namics: Application to the Development of Ovarian Follicles, SIAM J. Appl. Maths., 82(1):359–380,
2022.
[4] G. Ballif, F. Clément and R. Yvinec, nonlinear compartmental modeling to monitor ovarian follicle population dynamics on
the whole lifespan, hal-03739205.<a href="http://yvinec.perso.math.cnrs.fr/projects.html">Romain Yvinec</a> (INRAE, Physiologie de la Reproduction)2022-10-14T12:00:00-04:0012262mathematical biologyMathematical Biology SeminarFri, 14 Oct 2022 13:00:00 EDTFall, 2022Friday, October 14, 2022, 12:00pmPhysics 119Fri, 14 Oct 2022 12:00:00 EDTVertex functions as p-adic limits
https://services.math.duke.edu/mcal?abstract-12120
The vertex functions are generating functions counting numbers of rational curves in a quiver variety. In my talk I discuss a construction of certain polynomial solutions of hypergeometric equations modulo a prime p. I also describe a number of conjectures relating the p-adic limit of these solutions to the vertex functions of quiver varieties.
The talk is based on a joint investigation in progress with A. Varchenko.<a href="https://smirnov.web.unc.edu/">Andrey Smirnov</a> (UNC, Mathematics)2022-10-14T15:30:00-04:0012120algebraic geometryAlgebraic Geometry SeminarYesFall, 2022Fri, 14 Oct 2022 16:30:00 EDTGross 304BFri, 14 Oct 2022 15:30:00 EDTFriday, October 14, 2022, 3:30pmMarkov chains and sampling methods for contiguous partitions
https://services.math.duke.edu/mcal?abstract-12274
Markov chains have become an essential tool for sampling contiguous partitions of geometric regions, but there remains a dearth of rigorous results on the mixing times of the chains employed for this purpose. In this talk we'll discuss a sub-exponential bound on the mixing time of the Glauber dynamics chain for the case of bounded-size contiguous partition classes on certain grid-like classes of graphs.<a href="mailto:wes@math.cmu.edu">Wes Pegden</a> (CMU)2022-10-17T15:15:00-04:0012274probabilityProbability SeminarMon, 17 Oct 2022 16:15:00 EDTYesFall, 2022330 Gross HallMon, 17 Oct 2022 15:15:00 EDTMonday, October 17, 2022, 3:15pmA generalization of Geroch's conjecture
https://services.math.duke.edu/mcal?abstract-12197
Closed manifolds with topology N = M x S^1 do not admit metrics of positive Ricci curvature by the theorem of Bonnet-Myers, while the resolution of the Geroch conjecture implies that the torus T^n does not admit a metric of positive scalar curvature. In this talk we explain a non-existence result for metrics of positive m-intermediate curvature (a notion of curvature reducing to Ricci curvature for m = 1, and scalar curvature for m = n-1) on closed manifolds with topology N^n = M^{n-m} x T^m for n <= 7. Our proof uses minimization of weighted areas, the associated stability inequality, and delicate estimates on the second fundamental form. This is joint work with Simon Brendle and Sven Hirsch.<a href="mailto:johne@math.columbia.edu">Florian Johne</a> (Columbia University, Mathematics)2022-10-17T15:15:00-04:0012197geometry/topologyGeometry/topology SeminarFall, 2022Mon, 17 Oct 2022 16:15:00 EDTMonday, October 17, 2022, 3:15pmMon, 17 Oct 2022 15:15:00 EDTPhysics 119Putting Geometry on Collections of Data Points
https://services.math.duke.edu/mcal?abstract-12188
Tasks such as data alignment, gene expression analysis, time series analysis, and few-shot learning require means of comparing collections of data points, e.g. entire datasets or subpopulations of a single dataset. While optimal transport and related constructions provide means of lifting distances between data points to distances between point clouds, they can be computationally inefficient and are irrelevant when a metric for comparing individual data points is unavailable. In this talk, I will describe methods our group has developed for comparing collections of data points that are efficient and amenable to different applications. First, I will show how diffusion geometry can be used to compare datasets quickly, overcoming the cost of optimal transport when a quick comparison is sufficient. Second, I will show how a Riemannian metric on data can be inferred from population-level observations, inverting the typical transport-based lifting of distances from data points to datasets. Finally, I will share a recent project using the gradient of a machine learning model to put a geometry on data points that uncovers relevant minority groups and outliers.
Joint work with members of the MIT Geometric Data Processing group and the MIT-IBM Watson AI Lab.Justin Solomon (MIT)2022-10-18T15:15:00-04:0012188applied math and analysisApplied Math And Analysis SeminarTue, 18 Oct 2022 16:15:00 EDTFall, 2022Tuesday, October 18, 2022, 3:15pmTue, 18 Oct 2022 15:15:00 EDTPhysics 119Definible Analytic Spaces, 3
https://services.math.duke.edu/mcal?abstract-12289
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
https://Sakai.duke.edu/portal/site/htom<a href="https://www.hao-jia-umn-math.com/">Haohua Deng</a> (Duke University)2022-10-19T11:45:00-04:0012289Hodge TheoryLearning Seminar on Hodge Theory & O-MinimalityGross 304BWed, 19 Oct 2022 11:45:00 EDTWednesday, October 19, 2022, 11:45amWed, 19 Oct 2022 13:00:00 EDTFall, 2022Gergen Lecture 1: Euclidean traveller in hyperbolic worlds
https://services.math.duke.edu/mcal?abstract-12124
This lecture reports on a journey of an imaginary traveller, who travels along a Euclidean line. She will be travelling to many different geometric worlds such as the Euclidean n-torus guided by Kronecker in 1884, closed hyperbolic surfaces guided by Hedlund in 1936 and closed hyperbolic n-manifolds guided by Ratner in 1991. She also adventures into hyperbolic manifolds of infinite volume in the 21st century. We will describe what she sees (the closure of the line she travels on) and explain the mathematics involved in understanding the various closures with a number of illustrations.<a href="https://gauss.math.yale.edu/~ho2/">Hee Oh</a> (Yale)2022-10-19T15:15:00-04:0012124Gergen LecturesGergen Distinguished Lecture SeriesFall, 2022Wed, 19 Oct 2022 16:15:00 EDTWednesday, October 19, 2022, 3:15pmWed, 19 Oct 2022 15:15:00 EDTGross Hall 330, The Ahmediah Family Grand Hall(see Gergen Lectures)
https://services.math.duke.edu/mcal?abstract-12163
(see the Gergen Distinguished Lecture Series)Hee Oh 2022-10-19T15:15:00-04:0012163Number TheoryNumber Theory SeminarWed, 19 Oct 2022 15:15:00 EDTPhysics 119Wednesday, October 19, 2022, 3:15pmFall, 2022Wed, 19 Oct 2022 16:15:00 EDTGergen Lecture 2: Geometric prime number theorems
https://services.math.duke.edu/mcal?abstract-12125
The prime number theorem states that the number of primes of size at most T grows like T/log T, proved by Hadamard and de la Vallee Poussin in 1896. For Gaussian primes, that is, prime ideals in Z[i], not only does the number of Gaussian primes of norm at most T grow like T/logT but also the angular components of Gaussian primes are equidistributed in all directions, as proved by Hecke in 1920. Geometric analogues of these profound facts have been of great interest over the years. We will discuss effective versions of these theorems for hyperbolic 3-manifolds and for rational maps with many illustrations.<a href="https://gauss.math.yale.edu/~ho2/">Hee Oh</a> (Yale)2022-10-20T15:15:00-04:0012125Gergen LecturesGergen Distinguished Lecture SeriesGross Hall 330, The Ahmediah Family Grand HallThu, 20 Oct 2022 15:15:00 EDTThursday, October 20, 2022, 3:15pmThu, 20 Oct 2022 16:15:00 EDTFall, 2022Gergen Lecture 3: Apollonian circle packings
https://services.math.duke.edu/mcal?abstract-12126
An Apollonian circle packing is an ancient Greek construction which is made by repeatedly inscribing circles into the triangular interstices of four mutually tangent circles, via an old theorem of Apollonius of Perga (262-190 BC). We will discuss counting and equidistribution results for circles in Apollonian circle packings as well as some Diophantine questions for “integral” Apollonian packings.<a href="https://gauss.math.yale.edu/~ho2/">Hee Oh</a> (Yale)2022-10-21T12:00:00-04:0012126Gergen LecturesGergen Distinguished Lecture SeriesFri, 21 Oct 2022 13:00:00 EDTFall, 2022Gross Hall 330, The Ahmediah Family Grand HallFri, 21 Oct 2022 12:00:00 EDTFriday, October 21, 2022, 12:00pmCompetitive exclusion in a model with seasonality: three species cannot coexist in an ecosystem with two seasons
https://services.math.duke.edu/mcal?abstract-12264
Abstract: Chan, Durrett, and Lanchier introduced a multitype contact process with temporal heterogeneity involving two species competing for space on the d-dimensional integer lattice. Time is divided into two seasons. They proved that there is an open set of the parameters for which both species can coexist when their dispersal range is sufficiently large. Numerical simulations suggested that three species can coexist in the presence of two seasons. The main point of this paper is to prove that this conjecture is incorrect. To do this we prove results for a more general ODE model and contrast its behavior with other related systems that have been studied in order to understand the competitive exclusion principle.<a href="mailto:ht127@duke.edu">Ray Tung</a> (Duke University, Mathematics)2022-10-21T12:00:00-04:0012264mathematical biologyMathematical Biology SeminarFri, 21 Oct 2022 13:00:00 EDTFall, 2022https://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/12263.jpg" /></div>
Friday, October 21, 2022, 12:00pmFri, 21 Oct 2022 12:00:00 EDTPhysics 119Gergen Lecture 4: Rigidity of Kleinian groups
https://services.math.duke.edu/mcal?abstract-12251
Discrete subgroups of PSL(2,C) are called Kleinian groups. The famous Mostow rigidity theorem says that Kleinian groups of finite co-volume (=lattices) do not admit any faithful discrete representation into PSL(2,C) except for conjugations. I will present a new rigidity theorem for finitely generated Kleinian groups which are not necessarily lattices, and explain how this compares with Sullivan’s rigidity theorem.Hee Oh 2022-10-21T15:15:00-04:0012251Gergen LecturesGergen Lectures SeminarFri, 21 Oct 2022 16:15:00 EDTFall, 2022Gross Hall 330, The Ahmediah Family Grand HallFri, 21 Oct 2022 15:15:00 EDTFriday, October 21, 2022, 3:15pmBridging the gaps between homology planes and Mazur manifolds.
https://services.math.duke.edu/mcal?abstract-12174
We call a non-trivial homology 3-sphere a Kirby-Ramanujam sphere if it bounds a homology plane, an algebraic complex smooth surface with the same homology groups of the complex plane. In this talk, we present several infinite families of Kirby-Ramanujam spheres bounding Mazur type 4-manifolds, compact contractible smooth 4-manifolds built with only 0-, 1-, and 2-handles. Such an interplay between complex surfaces and 4-manifolds was first observed by Ramanujam and Kirby around nineteen-eighties. This is upcoming joint work with Rodolfo Aguilar Aguilar.<a href="https://sites.google.com/view/oguzsavk/homepage?pli=1">Oguz Savk</a> (Stanford University, Mathematics)2022-10-24T15:15:00-04:0012174geometry/topologyGeometry/topology SeminarMonday, October 24, 2022, 3:15pmZoom linkMon, 24 Oct 2022 15:15:00 EDTYesFall, 2022Mon, 24 Oct 2022 16:15:00 EDTMathematics in Blockchain
https://services.math.duke.edu/mcal?abstract-12259
There's a lot of buzz around the blockchain space these days.
Behind that buzz is a new technology built atop a variety of
interesting concepts from many different fields within
mathematics and computer science. In this talk, we will go
through a precise definition of what a blockchain *is*, the
mathematical concepts that make it work, the various kinds of
blockchains e.g. Bitcoin and Ethereum, and the future horizons
of how mathematics is helping improve these technologies.<a href="https://polygon.technology/solutions/polygon-zero/">Dmitry Vagner</a> (Polygon Zero)2022-10-24T17:00:00-04:0012259Public LecturesPublic Lectures Unveiling Math (PLUM)Mon, 24 Oct 2022 18:00:00 EDTFall, 2022YesMonday, October 24, 2022, 5:00pmMon, 24 Oct 2022 17:00:00 EDTPhysics 128TBA
https://services.math.duke.edu/mcal?abstract-12213
In-Jee Jeong (Seoul National University)2022-10-25T15:15:00-04:0012213applied math and analysisApplied Math And Analysis SeminarTuesday, October 25, 2022, 3:15pmPhysics 119Tue, 25 Oct 2022 15:15:00 EDTFall, 2022Tue, 25 Oct 2022 16:15:00 EDTDMI/MEMS Seminar
https://services.math.duke.edu/mcal?abstract-12280
Abstract:
The ability to organize diverse types of functional nanocomponents into the targeted architectures promises to enable a broad range of nanotechnological applications, from new classes of engineered biomaterials to photonic devices. However, the current top-down methods are limited in their ability to create 3D nanostructures with prescribed architecture and integration of different types of nanocomponents, while the typical bottom-up methods do not provide a flexibility of a system design. The talk will discuss an inverse design self-assembly strategies for the fabrication of large-scale and finite-size nano-architectures from diverse inorganic and biomolecular nanocomponents through the DNA-programmable approaches. The recent advances in creating periodic and hierarchical organizations from inorganic nanoparticles and proteins will be presented. The developed assembly approaches allow for creating functional nanomaterials with nano-optical, electrical, mechanical, and biochemical functions; some methods and examples of these efforts will be shown. Finally, the progress on establishing nanomaterial systems with prescribed transformation properties will be discussed.Oleg Gang (Columbia University)2022-10-26T12:00:00-04:0012280Other Meetings and EventsFall, 2022Wed, 26 Oct 2022 13:00:00 EDTNoneWed, 26 Oct 2022 12:00:00 EDTWednesday, October 26, 2022, 12:00pmOn an infinitesimal variant of Guo-Jacquet trace formulae
https://services.math.duke.edu/mcal?abstract-12230
A well-known theorem of Waldspurger relates central values of automorphic L-functions for GL(2) to automorphic period integrals over non-split tori. His result was reproved by Jacquet via the comparison of relative trace formulae. Guo-Jacquet’s conjecture aims to generalise Waldspurger’s result as well as Jacquet’s approach to higher dimensions. In this talk, we shall first recall the background of Guo-Jacquet trace formulae. Then we shall focus on an infinitesimal variant of these formulae and try to explain several results on the local comparison of most terms. Our infinitesimal study is expected to be relevant to the study of geometric sides of the original Guo-Jacquet trace formulae.<a href="mailto:hli213@jhu.edu">Huajie Li</a> (Johns Hopkins University, Mathematics)2022-10-26T15:15:00-04:0012230Department of MathematicsNumber TheoryNumber Theory SeminarWednesday, October 26, 2022, 3:15pmWed, 26 Oct 2022 15:15:00 EDTZoom linkWed, 26 Oct 2022 16:15:00 EDTYesFall, 2022Consistency Results for some Bayesian PDE inverse problems
https://services.math.duke.edu/mcal?abstract-12235
Frequently one would like to estimate functional parameters $u$ in a physical model defined by a partial differential equation from a collection of sparse and uncertain observations. Here a Bayesian methodology provides an attractive statistical approach for many such estimation problems, one which provides a comprehensive picture of uncertainties in the unknown. An important step in the validation of this Bayesian methodology is to establish conditions for posterior consistency. Specifically we would like to determine when $\mu_N \rightharpoonup \delta_{u_*}$ where $\mu_N$ is the Bayesian posterior conditioned on $N$ observations of the solution and $u_*$ is the true value of the unknown.
In this talk we describe some rigorous approaches that we have recently developed tailored to address consistency for PDE inverse problems involving the recovery of an infinite dimensional unknown. We describe how our approach applies to a gallery of model problems including the recovery of a divergence free velocity field from the measurement of a solute which is advecting and diffusing in the fluid medium. This is joint work with Jeff Borggaard, Christian Frederiksen and Justin Krometis.<a href="mailto:negh@tulane.edu">Nathan Glatt-Holtz</a> (Tulane University, Mathematics)2022-10-27T15:15:00-04:0012235probabilityProbability SeminarFall, 2022RTG21Thu, 27 Oct 2022 16:15:00 EDTPhysics 119Thu, 27 Oct 2022 15:15:00 EDTThursday, October 27, 2022, 3:15pmModelling pancreatic -cells: the symbiosis between electrical and metabolic activity
https://services.math.duke.edu/mcal?abstract-12266
Pancreatic -cells are responsible for maintaining the body's glucose homeostasis by secreting the hormone insulin. The insulin secretion results from coupling glucose metabolism to electrical activity via ATP-sensitive K+ channels. However, many of the factors that influence -cell function or insulin exocytosis are not fully understood. In the last three decades, several mathematical models have been developed to support the investigation.
In this talk, I will present the latest and more sophisticated of our models, the Integrated Oscillator Model (IOM), in which -cell electrical activity, intracellular Ca2+, and glucose metabolism interact via numerous feedforward and feedback pathways. I will then highlight how mathematical models can be used to both explain experimental results and design new experiments.<a href="https://www.birmingham.ac.uk/staff/profiles/metabolism-systems/Marinelli-Isabella.aspx">Isabella Marinelli</a> (Univ. Birmingham, Insitute of Metabolism and Systems Research)2022-10-28T12:00:00-04:0012266mathematical biologyMathematical Biology SeminarFall, 2022Fri, 28 Oct 2022 13:00:00 EDThttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/12265.png" /></div>
Friday, October 28, 2022, 12:00pmPhysics 119Fri, 28 Oct 2022 12:00:00 EDTThe knot complement problem for nullhomotopic knots
https://services.math.duke.edu/mcal?abstract-12270
In their celebrated work, Gordon and Luecke proved that knots in the three-dimensional sphere are determined by their complements. Subsequently, Boileau asked whether the same result holds for null-homotopic knots in arbitrary 3-manifolds. In this talk, I will discuss a program to answer this question. In particular, I will explain how one can give an affirmative answer to Boileau's question for arbitrary knots in some families of 3-manifolds including Lens spaces and Brieskorn homology spheres. This is joint work with Tye Lidman.<a href="https://www.math.wustl.edu/~adaemi/">Aliakbar Daemi</a> (Washington University in St.Louis, Mathematics)2022-10-31T15:15:00-04:0012270geometry/topologyGeometry/topology SeminarMon, 31 Oct 2022 15:15:00 EDTPhysics 119Monday, October 31, 2022, 3:15pmFall, 2022Mon, 31 Oct 2022 16:15:00 EDTDefinability of period maps
https://services.math.duke.edu/mcal?abstract-12290
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
https://Sakai.duke.edu/portal/site/htom<a href="mailto:robles@math.duke.edu">Colleen Robles</a> (Duke University)2022-11-02T11:45:00-04:0012290Hodge TheoryLearning Seminar on Hodge Theory & O-MinimalityWed, 02 Nov 2022 11:45:00 EDTGross 304BWednesday, November 2, 2022, 11:45amWed, 02 Nov 2022 13:00:00 EDTFall, 2022A density theorem towards p-adic monodromy
https://services.math.duke.edu/mcal?abstract-12205
We investigate the $p$-adic monodromy of certain kinds of abelian varieties in $\mathcal{A}_{g}$ and prove a formal density theorem for the locus of deformations with big monodromy. Also, we prove that the small monodromy locus of the deformation space of a supersingular elliptic curve is $p$-adic nowhere dense. The approach is based on a congruence condition of $p$-divisible groups and transform of data between the Rapoport-Zink spaces and deformation spaces.<a href="mailto:yfu68@wisc.edu">Jerry Yu Fu</a> (University of Wisconsin at Madison, Mathematics)2022-11-02T15:15:00-04:0012205Number TheoryNumber Theory SeminarWed, 02 Nov 2022 15:15:00 EDTPhysics 119Wednesday, November 2, 2022, 3:15pmYesFall, 2022Wed, 02 Nov 2022 16:15:00 EDTContaining the spread of a contagion on a tree
https://services.math.duke.edu/mcal?abstract-12248
Contact tracing can be thought of as a race between two processes: an infection process and a tracing process. In this paper, we study a simple model of infection spreading on a tree, and a tracer who stabilizes one node at a time. We focus on the question, how should the tracer choose nodes to stabilize so as to prevent the infection from spreading further? We study simple policies, which prioritize nodes based on time, infectiousness, or probability of generating new contacts. This talk is based on joint work with Jon Kleinberg.<a href="mailto:mcm377@cornell.edu">Michela Meister</a> (Cornell)2022-11-03T15:15:00-04:0012248probabilityProbability SeminarThu, 03 Nov 2022 16:15:00 EDTYesFall, 2022Zoom linkThu, 03 Nov 2022 15:15:00 EDTThursday, November 3, 2022, 3:15pmInvariant theory, rational singularities, and Hodge modules
https://services.math.duke.edu/mcal?abstract-12185
I want to talk about some work in progress with Scott Hiatt. For context, recall that given a reductive group G acting on a smooth complex algebraic variety, Boutot proved that the GIT quotient has rational singularities. This implies an earlier theorem of Hochster-Roberts that the quotient is Cohen-Macaulay. The analogue of Hochster-Roberts for modules, which has been considered by Stanley and
Van den Bergh, is somewhat subtle. Scott and I have recently found an extension of Boutot’s theorem for modules, or more precisely for Hodge modules that I will explain. We hope this will give more insight into the earlier work.<a href="https://www.math.purdue.edu/~arapura/">Donu Arapura</a> (Purdue U, Mathematics)2022-11-04T15:30:00-04:0012185algebraic geometryAlgebraic Geometry SeminarFriday, November 4, 2022, 3:30pmFri, 04 Nov 2022 15:30:00 EDTPhysics 119Fri, 04 Nov 2022 16:30:00 EDTFall, 2022YesAsymptotic bounds on the d-invariant
https://services.math.duke.edu/mcal?abstract-12134
As shown by Morita, every integral homology 3-sphere Y has a Heegaard decomposition into two handlebodies where the gluing map along the boundary is an element of the Torelli subgroup of the mapping class group of the boundary composed with the standard gluing map for the 3-sphere. In work in progress with Santana Afton and Tye Lidman, we show that the d-invariant of Y, a homology cobordism invariant of homology spheres defined using Heegaard Floer homology, is bounded above by a linear function of the word length of a corresponding gluing element in the Torelli group for any fixed, finite generating set when the genus is larger than 2. Moreover, we show the d-invariant is bounded for homology spheres corresponding to various large families of mapping classes.<a href="https://mkuzbary3.math.gatech.edu/">Miriam Kuzbary</a> (Georgia Tech, Mathematics)2022-11-07T15:15:00-05:0012134geometry/topologyGeometry/topology SeminarPhysics 119Mon, 07 Nov 2022 15:15:00 ESTMonday, November 7, 2022, 3:15pmhttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/11813.jpg" /></div>
Fall, 2022Mon, 07 Nov 2022 16:15:00 ESTStatistical reduced-order models and data-driven closure strategies for turbulent systems
https://services.math.duke.edu/mcal?abstract-12190
The capability of using imperfect statistical reduced-order models to capture crucial statistics in turbulent systems is investigated. Much simpler and more tractable block-diagonal models are proposed to approximate the complex and high-dimensional turbulent dynamical equations through parametric closure models. New machine learning strategies are proposed to learn the expensive unresolved processes directly from data. A systematic framework of correcting model errors with empirical information theory is introduced, and optimal model parameters under this unbiased information measure can be achieved in a training phase before the prediction. It is demonstrated that crucial principal statistical quantities in the most important large scales can be captured efficiently with accuracy using the reduced-order model in various dynamical regimes of the flow field with distinct statistical structures.Di Qi (Purdue)2022-11-08T15:15:00-05:0012190applied math and analysisApplied Math And Analysis SeminarTuesday, November 8, 2022, 3:15pmTue, 08 Nov 2022 15:15:00 ESTPhysics 119Tue, 08 Nov 2022 16:15:00 ESTFall, 2022Definable GAGA
https://services.math.duke.edu/mcal?abstract-12300
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
https://Sakai.duke.edu/portal/site/htom<a href="https://scholars.duke.edu/person/chunhsien.hsu">Chun-Hsien Hsu</a> (Duke University, Mathematics)2022-11-09T11:45:00-05:0012300Hodge TheoryLearning Seminar on Hodge Theory & O-MinimalityFall, 2022Wed, 09 Nov 2022 13:00:00 ESThttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/12299.jpg" /></div>
Wednesday, November 9, 2022, 11:45amWed, 09 Nov 2022 11:45:00 ESTGross 304BChow-Witt groups and quadratic refinements in motivic homotopy theory
https://services.math.duke.edu/mcal?abstract-12166
In the nineties, Voevodsky proposed a radical unification of
algebraic and topological methods. The amalgam of algebraic geometry and
homotopy theory that he and Fabien Morel developed is known as motivic
homotopy theory. Roughly speaking, motivic homotopy theory imports
methods from simplicial homotopy theory and stable homotopy theory into
algebraic geometry and uses the affine line to parameterize homotopies.
Voevodsky developed this theory with a specific objective in mind: prove
the Milnor conjecture. He succeeded in this goal and won the Fields
Medal for his efforts in 2002.
In this talk, I will start by recalling some facts in motivic homotopy
theory, and then present some results in motivic enumerative geometry
(Euler characteristic, trace formula, ramifications, computation of some
Chow-Witt groups, birational invariance). This is joint work with
Frédéric Déglise and Fangzhou Jin (see arXiv:2210.14832), and Tasos
Moulinos. Zoom notes: Meeting ID: 968 2220 8331Niels Feld 2022-11-09T15:15:00-05:0012166Number TheoryNumber Theory SeminarZoom linkWed, 09 Nov 2022 15:15:00 ESTWednesday, November 9, 2022, 3:15pmFall, 2022Wed, 09 Nov 2022 16:15:00 ESTBallistic Annihilation
https://services.math.duke.edu/mcal?abstract-12276
In the late 20th century, statistical physicists introduced a chemical reaction model called ballistic annihilation. In it, particles are placed randomly throughout the real line and then proceed to move at independently sampled velocities. Collisions result in mutual annihilation. Many results were inferred by physicists, but it wasn’t until recently that mathematicians joined in. I will describe my trajectory through this model. Expect tantalizing open questions.<a href="mailto:jungem13@gmail.com">Matt Junge</a> (Baruch College)2022-11-10T15:15:00-05:0012276probabilityProbability SeminarThu, 10 Nov 2022 15:15:00 ESTPhysics 119Thursday, November 10, 2022, 3:15pmYesFall, 2022Thu, 10 Nov 2022 16:15:00 ESTDeformations of singular Fano and Calabi-Yau varieties
https://services.math.duke.edu/mcal?abstract-12246
It is well known that Calabi-Yau manifolds have good deformation theory, which is controlled by Hodge theory. By work of Friedman, Namikawa, M. Gross, Kawamata, Steenbrink and others, some of these results have been extended to Calabi-Yau threefolds with canonical singularities. In this talk, I will report on further extensions in two directions: in dimension 3, we sharpen and clarify some of the existing results, and, secondly, we obtain some higher dimensional analogues. I will also briefly explain the related case of Fano varieties, where stronger results hold. One surprising aspect of our study is the role played by higher du Bois and higher rational singularities, notions that were recently introduced by Mustata, Popa, Saito and their collaborators.
<p>This is joint work with Robert Friedman.</p><a href="http://www.math.stonybrook.edu/~rlaza/">Radu Laza</a> (Stony Brook, Mathematics)2022-11-11T15:15:00-05:0012246algebraic geometryAlgebraic Geometry SeminarFall, 2022YesFri, 11 Nov 2022 16:15:00 ESTFriday, November 11, 2022, 3:15pmFri, 11 Nov 2022 15:15:00 ESTGross 304BMetric inequalities with positive scalar curvature
https://services.math.duke.edu/mcal?abstract-12195
In recent years, distance inequalities on Riemannian manifolds under a positive scalar curvature bound have become an important aspect in the study of scalar curvature, in particular, due to many new ideas and conjectures raised by Gromov. In this talk, I will mostly focus on Riemannian bands, that is, Riemannian manifolds diffeomorphic to N✕J, where N is a closed manifold and J is an interval. In the first part, I will use a perturbation of the Dirac method to show that, if N is a closed, connected spin n-manifold with non-vanishing Rosenberg index and g is a metric on N✕[-1,1] whose scalar curvature is bounded from below by n(n-1), then the distance between the two boundary components of N✕[-1,1] is at most 2𝜋/n. This gives, in many geometrically relevant cases, a sharp answer to a question raised by Gromov. In the last part of the talk, I will use a perturbation of the minimal hypersurface technique to show the following result. Let N be a closed, oriented n-manifold, with n≤7 and n≠4. If the cylinder N✕(-∞,∞) carries a complete metric of positive scalar curvature, then N carries a metric of positive scalar curvature. This establishes, up to dimension 7, a conjecture due to Rosenberg and Stolz. The results using the Dirac method are joint work with Rudolf Zeidler. The results using the minimal hypersurface method are joint work with Daniel Räde and Rudolf Zeidler.<a href="https://simonececchini.org/">Simone Cecchini</a> (Texas A&M University, Mathematics)2022-11-14T15:15:00-05:0012195geometry/topologyGeometry/topology SeminarMonday, November 14, 2022, 3:15pmPhysics 119Mon, 14 Nov 2022 15:15:00 ESTMon, 14 Nov 2022 16:15:00 ESTFall, 2022TBA
https://services.math.duke.edu/mcal?abstract-12161
Luis Martinez Zoroa (ICMAT)2022-11-15T15:15:00-05:0012161applied math and analysisApplied Math And Analysis SeminarPhysics 119Tue, 15 Nov 2022 15:15:00 ESTTuesday, November 15, 2022, 3:15pmFall, 2022Tue, 15 Nov 2022 16:15:00 ESTTBD
https://services.math.duke.edu/mcal?abstract-12302
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
https://Sakai.duke.edu/portal/site/htomTBD (Duke University, Mathematics)2022-11-16T11:45:00-05:0012302Hodge TheoryLearning Seminar on Hodge Theory & O-MinimalityFall, 2022Wed, 16 Nov 2022 13:00:00 ESTWed, 16 Nov 2022 11:45:00 ESTGross 304BWednesday, November 16, 2022, 11:45amDMI/MEMS Seminar
https://services.math.duke.edu/mcal?abstract-12294
Deep learning is revolutionizing many areas of science and technology, particularly in natural language processing, speech recognition, and computer vision. In this talk, we will provide an overview of the latest developments of machine learning and AI methods and their application to the problem of drug discovery and development at Isayev's Lab at CMU. We identify several areas where existing methods have the potential to accelerate materials research and disrupt more traditional approaches. First, we will present a deep learning model that approximates the solution of the Schrodinger equation. We introduce the AIMNet-NSE (Neural Spin Equilibration) architecture, which can predict molecular energies for an arbitrary combination of molecular charge and spin multiplicity. The AIMNet-NSE model allows us to bypass QM calculations fully and derive the ionization potential, electron affinity, and conceptual Density Functional Theory quantities like electronegativity, hardness, and condensed Fukui functions. We show that these descriptors, along with learned atomic representations, could be used to model chemical reactivity through an example of regioselectivity in electrophilic aromatic substitution reactions. Second, we proposed a novel ML-guided materials discovery platform that combines synergistic innovations in automated flow synthesis and automated machine learning (AutoML) method development. A software-controlled, continuous polymer synthesis platform enables rapid iterative experimental-computational cycles that result in the synthesis of hundreds of unique copolymer compositions within a multi-variable compositional space. The non-intuitive design criteria identified by ML, which was accomplished by exploring less than 0.9% of overall compositional space, upended conventional wisdom in the design of 19F MRI agents and led to the identification of >10 copolymer compositions that outperformed state-of-the-art materials.Olexandr Isayev (Carnegie Mellon University)2022-11-16T12:00:00-05:0012294Other Meetings and EventsNoneWed, 16 Nov 2022 12:00:00 ESTWednesday, November 16, 2022, 12:00pmWed, 16 Nov 2022 13:00:00 ESTFall, 2022CLASSIFICATION OF DISCRETE SERIES REPRESENTATIONS AND ITS APPLICATIONS ON THE GENERIC LOCAL LANGLANDS CORRESPONDENCE FOR ODD GSPIN GROUPS
https://services.math.duke.edu/mcal?abstract-12207
The classification of discrete series is one main subject in Langlands program
with numerous applications. We first explain the result on the classification of
discrete series of odd GSpin groups, generalizing the Mœglin-Tadi ́c classification
for classical groups. Note that our approach will give alternate proof for classical
groups. This is a joint work with Ivan Mati ́c. We also explain its application on
the generic local Langlands correspondence via Langlands-Shahidi method. If time
permits, we will explain possible generalization of those to other groups, which is work in progress<a href="mailto:ykim@chonnam.ac.kr">Yeansu Kim</a> (Purdue and Chonnam National University, Mathematics)2022-11-16T15:15:00-05:0012207Number TheoryNumber Theory SeminarWednesday, November 16, 2022, 3:15pmWed, 16 Nov 2022 15:15:00 ESTPhysics 119Wed, 16 Nov 2022 16:15:00 ESTYesFall, 2022Random Splitting of Fluid Models: Ergodicity, Convergence, and Chaos
https://services.math.duke.edu/mcal?abstract-12298
In this dissertation we study random splitting and apply our results to random splittings of fluid models. Random splitting is loosely defined as follows. Consider the differential equation $\dot{x}= V(x)$ where $\dot{x}$ is a time derivative and the vector field $V$ on $R^D$ splits as the sum $V=\sum_{j=1}^n V_j$. In traditional operator splitting one approximates solutions of $\dot{x}=V(x)$ by composing solutions of $\dot{x}=V_j(x)$ over (typically small)
deterministic time steps. Here we take these times to be independent and identically distributed random variables. This turns the aforementioned compositions into a Markov chain, which we call a random splitting of $V$ or simply random splitting. We prove under relatively mild conditions that these random splittings possess a unique invariant measure (ergodicity), that their trajectories converge on average and almost surely to trajectories of the original system $\dot{x}=V(x)$ (convergence), and that, in certain cases, their top Lyapunov exponent is positive (chaos). After proving these general results, we construct random splittings of four fluid models: the conservative Lorenz-96 and Lorenz-96 equations, and Galerkin approximations of the 2d Euler and 2d Navier-Stokes equations on the torus. We prove these random splittings are ergodic and converge to their deterministic counterparts in a certain sense, and, for
conservative Lorenz-96 and 2d Euler, that their top Lyapunov exponent is positive.Omar Melikechi (Duke University, Mathematics)2022-11-17T10:00:00-05:0012298Thesis DefensesThesis Defenses SeminarThursday, November 17, 2022, 10:00amThu, 17 Nov 2022 10:00:00 ESTPhysics 119Thu, 17 Nov 2022 12:00:00 ESTFall, 2022Cointegration, S&P, and random matrices
https://services.math.duke.edu/mcal?abstract-12239
Cointegration is a property of an N-dimensional time series, which says that
each individual component is non-stationary (growing like a random walk),
but there exists a stationary linear combination. Testing procedures for the
presence of cointegration has been extensively studied in statistics and
economics, but most results are restricted to the case when N is much
smaller than the length of the time series. I will discuss the recently
discovered mathematical structures, which make the large N case
accessible.<a href="mailto:vadicgor@gmail.com">Vadim Gorin</a> (UC Berkeley)2022-11-17T15:15:00-05:0012239probabilityProbability SeminarFall, 2022YesThu, 17 Nov 2022 16:15:00 ESTThu, 17 Nov 2022 15:15:00 ESTZoom linkThursday, November 17, 2022, 3:15pmThe Role of Stochasticity and System Size in Biological Systems
https://services.math.duke.edu/mcal?abstract-12296
Mathematical biologists seek to answer important questions about large, highly complex, and noisy biological systems. Scales of interest range from the dynamics of individual molecules to the interactions of huge ecological networks. Often, the size of these systems is exploited to derive much more tractable models in the appropriate mean field limit. I explore situations where small scale stochasticity impacts these very large biological systems in important and surprising ways. In the first part of this talk, I will introduce the generalized theory of extreme first passage times of many diffusing particles. I will show how many redundant searchers determine the timescale of important biological processes. I will then discuss both deterministic and stochastic models of chimeric antigen receptor (CAR) T-cell cancer therapy. I will demonstrate how treatment success is driven by stochastic extinction events when deterministic trajectories are driven into stochastic dominated regimes.<a href="mailto:madrid@math.utah.edu">Jacob Madrid</a> (University of Utah, Mathematics)2022-11-18T12:00:00-05:0012296mathematical biologyMathematical Biology Seminarby zoomFri, 18 Nov 2022 12:00:00 ESTFriday, November 18, 2022, 12:00pmhttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/12295.jpg" /></div>
Fall, 2022Fri, 18 Nov 2022 13:00:00 ESTOn opers and complex lagrangians
https://services.math.duke.edu/mcal?abstract-12118
In 2014 Gaiotto conjectured a lagrangian correspondence between holomorphic lagrangian of opers
in the Dolbeault moduli space of Higgs bundles and the de Rham moduli space of holomorphic connections, that is known today as conformal limit. This conjecture was established in 2016 for holomorphic opers.
In this talk I will present an algebraic geometry approach to conformal limits.
In rank 2, I will construct a holomorphic lagrangian foliation in the Hitchin moduli space based on the work of Simpson. This talk is based on joint work with Motohico Mulase.<a href="https://sites.google.com/site/oliviamireladumitrescu/">Olivia Dumitrescu</a> (UNC, Mathematics)2022-11-18T15:30:00-05:0012118algebraic geometryAlgebraic Geometry SeminarGross 304BFri, 18 Nov 2022 15:30:00 ESTFriday, November 18, 2022, 3:30pmFri, 18 Nov 2022 16:30:00 ESTYesFall, 2022Grid plabic graphs, Legendrian weaves, and (quasi-)cluster structures
https://services.math.duke.edu/mcal?abstract-12156
We construct a Legendrian link in R^3 from a “grid” plabic graph on R^2. We study a moduli space problem associated with the Legendrian link, and construct a natural (quasi-)cluster structure on this moduli space using Legendrian weaves. In particular, we prove that any braid variety associated with (beta Delta) for a 3-strand braid beta admits cluster structures with an explicit construction of initial seeds. We also construct Donaldson-Thomas transformations for these moduli spaces. In this talk, I will introduce the theoretical background and describe the basic combinatorics for constructing Legendrian weaves and the (quasi-)cluster structures from a grid plabic graph. This is based on a joint work with Roger Casals (arXiv:2204.13244).<a href="https://www.math.ucdavis.edu/~daping/">Daping Weng</a> (University of California, Davis)2022-11-21T15:15:00-05:0012156geometry/topologyGeometry/topology SeminarMon, 21 Nov 2022 16:15:00 ESTFall, 2022IntMonday, November 21, 2022, 3:15pmMon, 21 Nov 2022 15:15:00 ESTPhysics 119Homology cobordism and knot concordance
https://services.math.duke.edu/mcal?abstract-12131
The 0-surgeries of two knots K1 and K2 are homology cobordant rel meridians if there exists an integer homology cobordism X between them such that the two positive knot meridians are in the same homology class of X. It is a natural question to ask: if two knots have the “same” 0-surgeries in this sense, must they be smoothly concordant? We give a pair of knots as counterexample, with one of concordance order two and the other of infinite order, and along the way expand upon a Floer homology technique for obstructing torsion in the smooth concordance group first introduced by Hom, Kang, Park, and Stoffregen.<a href="https://sites.google.com/view/sarah-sally-collins/home">Sally Collins</a> (Georgia Tech, Mathematics)2022-11-28T15:15:00-05:0012131geometry/topologyGeometry/topology SeminarMon, 28 Nov 2022 16:15:00 ESTFall, 2022Physics 119Mon, 28 Nov 2022 15:15:00 ESTMonday, November 28, 2022, 3:15pmAdvances in immersed methods for fluid-structure interaction
https://services.math.duke.edu/mcal?abstract-12237
The immersed boundary (IB) method is a framework for modeling systems in which an elastic structure interacts with a viscous incompressible fluid. The fundamental feature of the IB approach to such fluid-structure interaction (FSI) problems is its combination of an Eulerian formulation of the momentum equation and incompressibility constraint with a Lagrangian description of the structural deformations and resultant forces. In conventional IB methods, Eulerian and Lagrangian variables are linked through integral equations with Dirac delta function kernels, and these singular kernels are replaced by regularized delta functions when the equations are discretized for computer simulation. This talk will focus on three related extensions of the IB method. I first detail an IB approach to structural models that use the framework of large-deformation nonlinear elasticity. I will focus on efficient numerical methods that enable finite element structural models in large-scale simulations, with examples focusing on models of the heart and its valves. Next, I will describe an extension of the IB framework to simulate soft material failure using peridynamics, which is a nonlocal structural mechanics formulation. Numerical examples demonstrate constitutive correspondence with classical mechanics for non-failure cases along with essentially grid-independent predictions of fluid-driven soft material failure. Finally, I will introduce a reformulation of the IB large-deformation elasticity framework that enables accurate and efficient fluid-structure coupling through a version of the immersed interface method, which is a sharp-interface IB-type method. Computational examples demonstrate the ability of this methodology to simulate a broad range of fluid-structure mass density ratios without suffering from artificial added mass instabilities, and to facilitate subgrid contact models. I will also present biomedical applications of the methodology, including models of clot capture by inferior vena cava filters.Boyce Griffith (UNC Chapel Hill)2022-11-29T15:15:00-05:0012237applied math and analysisApplied Math And Analysis SeminarFall, 2022Tue, 29 Nov 2022 16:15:00 ESTTue, 29 Nov 2022 15:15:00 ESTPhysics 119Tuesday, November 29, 2022, 3:15pmTBD
https://services.math.duke.edu/mcal?abstract-12303
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
https://Sakai.duke.edu/portal/site/htomTBD (Duke University, Mathematics)2022-11-30T11:45:00-05:0012303Hodge TheoryLearning Seminar on Hodge Theory & O-MinimalityFall, 2022Wed, 30 Nov 2022 13:00:00 ESTGross 304BWed, 30 Nov 2022 11:45:00 ESTWednesday, November 30, 2022, 11:45amMarkoff-type K3 Surfaces: Local and Global Finite Orbits
https://services.math.duke.edu/mcal?abstract-12288
Markoff triples were introduced in 1879 and have a rich history spanning many branches of mathematics. In 2016, Bourgain, Gamburd, and Sarnak answered a long standing question by showing there exist infinitely many composite Markoff numbers. Their proof relied on showing the connectivity for an infinite family of graphs associated to Markoff triples modulo p for infinitely many primes p. In this talk we discuss what happens for the projective analogue of Markoff triples, that is surfaces W in P^1 x P^1 x P^1 cut out by the vanishing of a (2,2,2)-form that admit three non-commuting involutions and are fixed under coordinate permutations and double sign changes. Inspired by the work of B-G-S we investigate such surfaces over finite fields, specifically their orbit structure under their automorphism group. For a specific one-parameter subfamily W_k of such surfaces, we construct finite orbits in W_k(C) by studying small orbits that appear in W_k(F_p) for many values of p and k. This talk is based on joint work with E. Fuchs, J. Silverman, and A. Tran.<a href="https://www.math.ucdavis.edu/~mclitman/">Matthew Litman</a> (University of California, Davis, Mathematics)2022-11-30T15:15:00-05:0012288Number TheoryNumber Theory SeminarPhysics 119Wed, 30 Nov 2022 15:15:00 ESTWednesday, November 30, 2022, 3:15pmWed, 30 Nov 2022 16:15:00 ESTFall, 2022YesDMI/MRS Seminar
https://services.math.duke.edu/mcal?abstract-12322
Abstract:
The overall goal of my research is to study and understand reactive, multiphase transport in porous materials. Of particular interest is manipulating chemical and physical processes that occur during reactive, multiphase transport in both engineered (cementitious) and natural (geological) porous materials. To this end, quantitative imaging approaches such as X-ray computed tomography (CT), neutron tomography, electrical imaging modalities, and simultaneous imaging are powerful tools to obtain complementary information with temporal context to better understand complex changes within materials.
This presentation will provide an overview of three-dimensional (3D) imaging techniques and how these modalities are used to study changes in porous materials with time (four-dimensional, 4D). Numerous porous materials are utilized to construct the built environment, including cement-based materials (concrete and foamed cement [a non-Newtonian fluid in slurry form]), wood, asphalt concrete, and geological materials (sandstones, limestone) among others. From characterizing pore size distribution evolution and quantifying the kinetics of water sorption in cement-based materials to studying reactive transport in both cement-based and geological materials used for Carbon Capture and Storage (CCS), 4D imaging provides a powerful tool to further our understanding of material properties, material behavior, and enable the development of new materialsLaura Dalton 2022-12-01T17:00:00-05:0012322Other Meetings and EventsThu, 01 Dec 2022 18:00:00 ESTFall, 2022Fitzpatrick Center Schiciano Auditorium Side A, room 1464Thu, 01 Dec 2022 17:00:00 ESTThursday, December 1, 2022, 5:00pmSymmetric Formulas for Products of Permutations
https://services.math.duke.edu/mcal?abstract-12310
We will discuss the computational complexity of multiplying a sequence of permutation matrices. This computational problem exhibits natural symmetries, and the smallest known Boolean formulas for this problem also exhibit these symmetries. In recent work we have proved that with this symmetry constraint, these smallest known formulas are optimal, and in this talk we will give an overview of the proof.William He 2022-12-02T11:00:00-05:0012310Thesis DefensesThesis Defenses SeminarFri, 02 Dec 2022 12:00:00 ESTFall, 2022Friday, December 2, 2022, 11:00amFri, 02 Dec 2022 11:00:00 ESTLSRC D243Anosov groups and Hodge theory
https://services.math.duke.edu/mcal?abstract-12178
Discrete subgroups of Lie groups are much-studied and appear throughout mathematics. Anosov subgroups form a class which is intermediate between lattices in higher rank semisimple Lie groups and Fuchsian subgroups of SL(2,R) that uniformize Riemann surfaces. After providing the necessary background, I will explain how Anosov groups can arise as monodromies of families of algebraic manifolds and how this phenomenon is related to Hodge theory. I will then describe some uniformization results for "non-classical" variations of Hodge structure and explain some (simple to state) consequences for the algebraic geometry of the underlying family.<a href="https://math.uchicago.edu/~sfilip">Simion Filip</a> (U Chicago, Mathematics)2022-12-02T12:00:00-05:0012178ColloquiumColloquium SeminarFri, 02 Dec 2022 13:00:00 ESTFall, 2022YesFri, 02 Dec 2022 12:00:00 ESTGross Hall 330, The Ahmediah Family Grand HallFriday, December 2, 2022, 12:00pmData Assimilation and Dynamical Systems Analysis of Circadian Rhythmicity and Entrainment
https://services.math.duke.edu/mcal?abstract-12320
Circadian rhythms are biological oscillations that align our physiology and behavior with the 24-hour environmental cycles conferred by the Earth’s rotation. In this talk, I will discuss two projects that focus on circadian clock cells in the brain and the entrainment of circadian rhythms to the light-dark cycle. Most of what we know about the electrical activity of circadian clock neurons comes from studies of nocturnal (night-active) rodents, hindering the translation of this knowledge to diurnal (day-active) humans. In the first part of the talk, we use data assimilation and patch-clamp recordings from the diurnal rodent Rhabdomys pumilio to build the first mathematical models of the electrophysiology of circadian neurons in a day-active species. We find that the electrical activity of circadian neurons is similar overall between nocturnal and diurnal rodents but that there are some interesting differences in their responses to inhibition. In the second part of the talk, we use tools from dynamical systems theory to study the reentrainment of a model of the human circadian pacemaker following perturbations that simulate jet lag. We show that the reentrainment dynamics are organized by invariant manifolds of fixed points of a 24-hour stroboscopic map and use these manifolds to explain a rapid reentrainment phenomenon that occurs under certain jet lag scenarios.<a href="https://web.njit.edu/~diekman/research.html">Casey Diekman</a> (New Jersey Institute of Technology, Mathematics)2022-12-02T12:00:00-05:0012320mathematical biologyMathematical Biology SeminarFriday, December 2, 2022, 12:00pmPhysics 119Fri, 02 Dec 2022 12:00:00 ESTFri, 02 Dec 2022 13:00:00 ESTFall, 2022https://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/12319.jpg" /></div>
Uniformization of some higher weight variations of Hodge structure
https://services.math.duke.edu/mcal?abstract-12179
I will explain some differential-geometric techniques and results that can be used to give uniformizations of some variations of Hodge structure with Hodge numbers (1,1,1,1). In particular, I will explain how local conditions on the Kodaira-Spencer maps imply that the monodromy representation is "Anosov", which is a global geometric property.
The methods apply for example to the mirror quintic (aka Dwork, aka Fermat) family and yield a strong Torelli theorem, as well as a number of further consequences.<a href="https://math.uchicago.edu/~sfilip">Simion Filip</a> (U Chicago, Mathematics)2022-12-02T15:30:00-05:0012179algebraic geometryAlgebraic Geometry SeminarFri, 02 Dec 2022 16:30:00 ESTFall, 2022YesFriday, December 2, 2022, 3:30pmGross 304BFri, 02 Dec 2022 15:30:00 ESTMathematics for Human Flourishing
https://services.math.duke.edu/mcal?abstract-12308
Math is more than just a way to describe the world, and it is more than just a set of skills, like doing arithmetic or factoring a quadratic. Math is a deeply human enterprise that fulfills basic human longings, such as for beauty and exploration and truth, and when properly engaged, it builds virtues like persistence, creativity, and a competence to solve problems you've never seen before. Reframing math in this way---around virtues---offers a more attractive way to welcome people to see math as an intrinsic part of life, and to teach it in a more equitable, inclusive way. An incarcerated man---now my friend---has helped me see this more clearly than ever before. This event is sponsored by Duke Faculty Advancement Seed Grant Program.<a href="https://math.hmc.edu/su/">Francis Su</a> (Harvey Mudd College, Mathematics)2022-12-02T17:00:00-05:0012308Other Meetings and EventsOther Meetings And Events Seminarhttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/12307.jpg" /></div>
Fall, 2022Fri, 02 Dec 2022 18:00:00 ESTFri, 02 Dec 2022 17:00:00 ESTPhysics 128Friday, December 2, 2022, 5:00pmCoherent orientations of DGA maps associated to exact Lagrangian cobordisms
https://services.math.duke.edu/mcal?abstract-12256
We discuss the DGA map induced by an exact Lagrangian cobordism, and an analytic strategy to lift the map to integer coefficients, introduced by Fukaya, Oh, Ohta and Ono and further adapted by Ekholm, Etnyre, and Sullivan and Karlsson respectively. We then explain how this strategy can be applied to find a concrete combinatorial formula for a mini-dipped pinch move, thereby completely determining the integral DGA maps for all decomposable, orientable Lagrangian cobordisms. If time permits, we will show how to obtain this formula in a model case. We will also go into future potential work, including applications to Heegaard Floer Homology and nonorientable cobordisms.<a href="https://sites.google.com/view/chindu-mohanakumar/home?pli=1">Chindu Mohanakumar</a> (Duke)2022-12-05T15:15:00-05:0012256geometry/topologyGeometry/topology SeminarMon, 05 Dec 2022 16:15:00 ESTFall, 2022YesMonday, December 5, 2022, 3:15pmMon, 05 Dec 2022 15:15:00 ESTPhysics 119New approaches in simulation of transition paths
https://services.math.duke.edu/mcal?abstract-12192
Tensor method can be used for compressing high-dimensional functions arising from partial differential equations (PDE). In this talk, we focus on using these methods for the simulation of transition processes between metastable states in chemistry applications, for example in molecular dynamics. To this end, we also propose a novel generative modeling procedure using tensor-network without the use of any optimization.Yuehaw Khoo (Chicago)2022-12-06T15:15:00-05:0012192applied math and analysisApplied Math And Analysis SeminarTuesday, December 6, 2022, 3:15pmPhysics 119Tue, 06 Dec 2022 15:15:00 ESTFall, 2022Tue, 06 Dec 2022 16:15:00 ESTTBD
https://services.math.duke.edu/mcal?abstract-12304
Learning seminar topics to include introduction to Hodge theory, introduction to o-minimality; nilpotent and SL(2) orbit theorems, Hodge norm estimates; definability of period maps, and quasi-projectivity of the image.
Organized by Dr. Haohua Deng [haohua.deng@duke.edu].
https://Sakai.duke.edu/portal/site/htomTBD (Duke University, Mathematics)2022-12-07T11:45:00-05:0012304Hodge TheoryLearning Seminar on Hodge Theory & O-MinimalityWed, 07 Dec 2022 11:45:00 ESTGross 304BWednesday, December 7, 2022, 11:45amWed, 07 Dec 2022 13:00:00 ESTFall, 2022Moments of Dirichlet L-functions
https://services.math.duke.edu/mcal?abstract-12164
In recent decades there has been much interest and measured progress in the study of moments of L-functions. Despite a great deal of effort spanning over a century, asymptotic formulas for moments of L-functions remain stubbornly out of reach in all but a few cases. I will begin this talk by reviewing what is known for moments of the Riemann zeta-function on the critical line, and we will then consider the problem for the family of all Dirichlet L-functions of even primitive characters of bounded conductor. A heuristic of Conrey, Farmer, Keating, Rubenstein, and Snaith gives a precise prediction for the asymptotic formula for the general 2kth moment of this family. I will outline how to harness the asymptotic large sieve to prove an asymptotic formula for the general 2kth moment of approximations of this family. The result, which assumes the generalized Lindelöf hypothesis for large values of k, agrees with the prediction of CFKRS. Moreover, it provides the first rigorous evidence beyond the so-called “diagonal terms” in their conjectured asymptotic formula for this family of L-functions. This is joint work with Siegfred Baluyot and a product of the NSF Focused Research Group “Averages of L-functions and Arithmetic Stratification.”<a href="mailto:cturnageb@carleton.edu">Caroline Turnage-Butterbaugh</a> 2022-12-07T15:15:00-05:0012164Number TheoryNumber Theory SeminarWed, 07 Dec 2022 16:15:00 ESTIntFall, 2022Physics 119Wed, 07 Dec 2022 15:15:00 ESTWednesday, December 7, 2022, 3:15pmPL surfaces and genus cobordism
https://services.math.duke.edu/mcal?abstract-12312
Every knot in S^3 bounds a PL disk in the four ball. But this is no longer true for knots in other three manifolds, as demonstrated first by Akbulut, who constructed a knot which does not bound any PL disk in a specific contractible four manifold. Then Levine showed that there exist knots that do not bound a PL disk in any homology four ball. What happens if we relax the condition of bounding PL disk to bounding a PL surface with some given genus? In the joint work with Hom and Stoffregen, we proved that for each n, there exists a knot K_n in an integer homology sphere that does not bound a PL surface of genus n in any homology four ball. The proof uses Heegaard Floer homology. More specifically, the obstruction comes from knot cobordism maps by Zemke and the construction uses recent filtered mapping cone formula for cables of the knot meridian.<a href="https://sites.google.com/view/hzhou/home">Hugo Zhou</a> (Georgia Tech, Mathematics)2022-12-12T15:15:00-05:0012312geometry/topologyTriangle TopologyGeometry/topology SeminarFall, 2022YesMon, 12 Dec 2022 16:15:00 ESTMonday, December 12, 2022, 3:15pmMon, 12 Dec 2022 15:15:00 ESTPhysics 119Fast Matrix Multiplication That Does Not Slow Down
https://services.math.duke.edu/mcal?abstract-12336
In the world of Pokémon, trainers often rely on their trusty Pokémon to battle against other trainers and their Pokémon. However, when a trainer wants to defeat a particularly powerful opponent, they may need to combine the strengths of multiple Pokémon to overcome their enemy. This is similar to how distributed matrix multiplication (DMM) works. In DMM, multiple machines work together to quickly calculate the product of two matrices. But just like a Pokémon trainer, it's important to have a backup plan in case one of the machines fails or loses connection. That's why we propose a hybrid algorithm that combines DMM with fast matrix multiplication (FMM). This combination allows us to take the best of both worlds, providing both speed and reliability. By analyzing the tensor product code structure of the hybrid algorithm, we can prove that it has a positive error exponent, meaning it can withstand errors and continue to function effectively. So just like a trainer would carefully select the right Pokémon for the job, we've chosen the perfect combination of DMM and FMM to quickly and reliably calculate matrix products.Hsin-Po Wang 2022-12-13T12:00:00-05:0012336Other Meetings and EventsiiD SeminarTue, 13 Dec 2022 13:00:00 ESTFall, 2022Tue, 13 Dec 2022 12:00:00 ESTGross Hall, Ahmadieh Family Grand Hall, Room 330Tuesday, December 13, 2022, 12:00pmPositroids, knots, and q,t-Catalan numbers
https://services.math.duke.edu/mcal?abstract-12333
Open positroid varieties are certain subvarieties of the Grassmannian that arise in the study of total positivity and have surprising applications in many areas of mathematics and physics. After reviewing some history and background, I will discuss our recent joint work with Thomas Lam relating the cohomology of these varieties and their point counts over finite fields to knot invariants such as the HOMFLYPT polynomial and Khovanov–Rozansky homology. In particular, we show that the bigraded Poincaré polynomials of top-dimensional open positroid varieties are given by rational q,t-Catalan numbers. <font color="red">No background on the above objects will be assumed.</font><a href="https://www.math.ucla.edu/~galashin/papers.html">Pavel Galashin</a> (University of California at Los Angeles, Mathematics)2022-12-13T14:00:00-05:0012333Other Meetings and EventsOther Meetings And Events SeminarPhysics 119Tue, 13 Dec 2022 14:00:00 ESTTuesday, December 13, 2022, 2:00pmFall, 2022Tue, 13 Dec 2022 15:00:00 ESTExponential mixing by shear flows
https://services.math.duke.edu/mcal?abstract-12886
Given a divergence-free vector field on the torus, we consider the mixing properties of the associated flow. There is a rich body of work studying the dependence of the mixing scale on various norms of the vector field. We will discuss some examples of particularly simple vector fields that mix at the optimal rate, and an improved lower bound on the mixing scale under the extra assumption that the vector field is a shear at each time.William Cooperman (University of Chicago)2022-12-13T15:15:00-05:0012886applied math and analysisApplied Math And Analysis SeminarFall, 2022Tue, 13 Dec 2022 16:15:00 ESTPhysics 119Tue, 13 Dec 2022 15:15:00 ESTTuesday, December 13, 2022, 3:15pmAlgebraically closed fields in higher algebra
https://services.math.duke.edu/mcal?abstract-12325
Higher algebra is a homotopical enlargement of algebra where algebraic structures, such as rings and modules, have underlying spaces as opposed to just underlying sets. A striking feature of higher algebra is that there are additional "chromatic characteristics" interpolating between characteristic 0 and characteristic p. These intermediate characteristics have shed light on mod p phenomena in geometry, number theory, and representation theory. At the same time, the extension of algebraic ideas to higher algebra has been fruitful within algebraic topology: I will discuss joint work with Robert Burklund and Tomer Schlank which proves a higher analogue of Hilbert’s Nullstellensatz, thus identifying the algebraically closed fields of intermediate characteristic. In addition to initiating the study of "chromatic algebraic geometry," this work resolves a form of Rognes’ chromatic redshift conjecture in algebraic K-theory.<a href="https://allenyuan.me">Allen Yuan</a> (Columbia University, Mathematics)2022-12-16T17:30:00-05:0012325Other Meetings and EventsMath/StatisticsOther Meetings And Events SeminarFall, 2022Fri, 16 Dec 2022 18:30:00 ESTFri, 16 Dec 2022 17:30:00 ESTPhysics 119Friday, December 16, 2022, 5:30pmCombinatorial Aspects of Determinantal Varieties
https://services.math.duke.edu/mcal?abstract-12328
Schubert calculus has its origins in enumerative questions asked by the geometers of the 19th century, such as “how many lines meet four fixed lines in three-space?” These problems can be recast as questions about the structure of cohomology rings of geometric spaces such as flag varieties. Borel’s isomorphism identifies the cohomology of the complete flag variety with a simple quotient of a polynomial ring. Lascoux and Schützenberger (1982) defined Schubert polynomials, which are coset representatives for the Schubert basis of this ring. However, it was not clear if this choice was geometrically natural. Knutson and Miller (2005) provided a justification for the naturality of Schubert polynomials via antidiagonal Gröbner degenerations of matrix Schubert varieties, which are generalized determinantal varieties. Furthermore, they showed that pre-existing combinatorial objects called pipe dreams govern this degeneration. In this talk, we study the dual setting of diagonal Gröbner degenerations of matrix Schubert varieties, interpreting these limits in terms of the “bumpless pipe dreams” of Lam, Lee, and Shimozono (2021). We then use the combinatorics of K-theory representatives for Schubert classes to compute the Castelnuovo-Mumford regularity of matrix Schubert varieties, which gives a bound on the complexity of their coordinate rings.<a href="https://math.mit.edu/~weigandt/">Anna Weigandt</a> (MIT, Mathematics)2022-12-20T12:00:00-05:0012328Other Meetings and EventsOther Meetings And Events SeminarFall, 2022Tue, 20 Dec 2022 13:00:00 ESTTue, 20 Dec 2022 12:00:00 ESTPhysics 119Tuesday, December 20, 2022, 12:00pmDepartment [DELETED]
https://services.math.duke.edu/mcal?abstract-12979
Dept. Faculty Meeting 2024-03-22T10:30:00-04:0012979Department of MathematicsR.BryantSpring, 2024Fri, 22 Mar 2024 11:30:00 EDTdeletedFriday, March 22, 2024, 10:30amPhysics 119Fri, 22 Mar 2024 10:30:00 EDTTBA [DELETED]
https://services.math.duke.edu/mcal?abstract-12849
Zoom link: TBA<a href="https://www.ihes.fr/~urbanik/">David Urbanik</a> (IHES)2024-03-29T13:30:00-04:0012849algebraic geometryAlgebraic Geometry SeminarZoom linkFri, 29 Mar 2024 13:30:00 EDTFriday, March 29, 2024, 1:30pmdeletedSpring, 2024Fri, 29 Mar 2024 14:30:00 EDTTBA [DELETED] --- CANCELED
https://services.math.duke.edu/mcal?abstract-12874
<a href="https://spencerleslie.com/">Spencer Leslie</a> (Boston College, Mathematics)2024-04-10T15:15:00-04:0012874Number TheoryNumber Theory SeminardeletedIntSpring, 2024Wed, 10 Apr 2024 15:15:00 EDTPhysics 119Wed, 10 Apr 2024 15:15:00 EDTWednesday, April 10, 2024, 3:15pmTBA [DELETED]
https://services.math.duke.edu/mcal?abstract-12956
<a href="https://sites.google.com/view/jpark776/home">Jaemin Park</a> (University of Basel)2024-04-23T15:15:00-04:0012956Department of Mathematicsapplied math and analysisDepartment of Mathematics SeminarPhysics 119Tue, 23 Apr 2024 15:15:00 EDTTuesday, April 23, 2024, 3:15pmdeletedSpring, 2024Tue, 23 Apr 2024 16:15:00 EDT [DELETED]
https://services.math.duke.edu/mcal?abstract-12872
Mary Pugh (University of Pennsylvania)2024-05-11T11:00:00-04:0012872Department of MathematicsGraduation "SAVE THE DATE"Sat, 11 May 2024 11:00:00 EDTOnsiteSaturday, May 11, 2024, 11:00amdeletedSat, 11 May 2024 14:00:00 EDTSpring, 2024