Department of Mathematics, Duke University

• Monday, April 23, 2018, 3:15pm, 119 Physics, Geometry/topology Seminar
  Asymptotic geometry of hyperpolygons
  Steven Rayan (University of Saskatchewan, Department of Mathematics & Statistics)

   

  Nakajima quiver varieties lie at the interface of geometry and representation theory and provide an important class of examples of Calabi-Yau manifolds. I will discuss a particular instance, hyperpolygon space, which arises from a certain shape of quiver. The simplest of these is a noncompact complex surface admitting the structure of an "instanton", and therefore fits nicely into the Kronheimer-Nakajima classification of ALE hyperkaehler 4-manifolds, which is a geometric realization of the McKay correspondence for finite subgroups of SU(2). For more general hyperpolygon spaces, we can speculate on how this classification might be extended by studying the geometry of hyperpolygons at "infinity". This talk represents previous work with Jonathan Fisher and ongoing work with Hartmut Weiss.

• Tuesday, April 24, 2018, 3:00pm, 119 Physics, CNCS Seminar
  When is the Gardner transition relevant?
  Camille Scalliet (University de Montpellier, Physics)

   

  The idea that glasses can become marginally stable at a Gardner transition has attracted significant interest among the glass community. Yet, the situation is confusing: even at the theoretical level, renormalization group approaches provide contradictory results on whether the transition can exist in three dimensions. The Gardner transition was searched in only two experimental studies and few specific numerical models. These works lead to different conclusions for the existence of the transition, resulting in a poor understanding of the conditions under which a marginally stable phase can be observed. The very relevance of the Gardner transition for experimental glasses is at stake.

  We study analytically and numerically the Weeks-Chandler-Andersen model. By changing external parameters, we continuously explore the phase diagram and regimes relevant to granular, colloidal, and molecular glasses. We revisit previous numerical studies and confirm their conclusions. We reconcile previous results and rationalise under which conditions a Gardner phase can be observed. We find that systems in the vicinity of a jamming transition possess a Gardner phase. Our findings confirm the relevance of a Gardner transition for colloidal and granular glasses, and encourage future experimental work in this direction. For molecular glasses, we find that no Gardner phase is present, but our studies reveal instead the presence of localised excitations presumably relevant for mechanical and vibrational properties of glasses.

• Wednesday, April 25, 2018, 12:00pm, Physics 119, Applied Math And Analysis Seminar
  Understanding Manifold-structured Data via Geometric Modeling and Learning
  Rongjie Lai (Rensselaer Polytechnic Institute)

   

  Analyzing and inferring the underlying global intrinsic structures of data from its local information are critical in many fields. In practice, coherent structures of data allow us to model data as low dimensional manifolds, represented as point clouds, in a possible high dimensional space. Different from image and signal processing which handle functions on flat domains with well-developed tools for processing and learning, manifold-structured data sets are far more challenging due to their complicated geometry. For example, the same geometric object can take very different coordinate representations due to the variety of embeddings, transformations or representations (imagine the same human body shape can have different poses as its nearly isometric embedding ambiguities). These ambiguities form an infinite dimensional isometric group and make higher-level tasks in manifold-structured data analysis and understanding even more challenging. To overcome these ambiguities, I will first discuss modeling based methods. This approach uses geometric PDEs to adapt the intrinsic manifolds structure of data and extracts various invariant descriptors to characterize and understand data through solutions of differential equations on manifolds. Inspired by recent developments of deep learning, I will also discuss our recent work of a new way of defining convolution on manifolds and demonstrate its potential to conduct geometric deep learning on manifolds. This geometric way of defining convolution provides a natural combination of modeling and learning on manifolds. It enables further applications of comparing, classifying and understanding manifold-structured data by combing with recent advances in deep learning.

• Thursday, April 26, 2018, 9:00am, Physics 128, The Fourth Duke Mathematical Journal Conference
  The Fourth Duke Mathematical Journal Conference
  Various

   

  The talks will cover an array of subject areas that are well-represented in the Duke Journal. There will be nine talks by young mathematicians. These speakers are: Emmanuel Breuillard (Munster) Ivan Corwin (Columbia) Alessio Figalli (Zurich) John Pardon (Princeton) Lu Wang (Wisconsin) Melanie Matchett Wood (Wisconsin) Giulia Saccà (MIT) Alex Wright (Stanford) Zhiwei Yun (Yale)

• Thursday, April 26, 2018, 3:15pm, 119 Physics, Probability Seminar
  Particles interacting through their hitting times: neuron firing, supercooling and systemic risk
  Mykhaylo Shkolnikov (Princeton University)

   

  I will discuss a class of particle systems that serve as models for supercooling in physics, neuron firing in neuroscience and systemic risk in finance. The interaction between the particles falls into the mean-field framework pioneered by McKean and Vlasov in the late 1960s, but many new phenomena arise due to the singularity of the interaction. The most striking of them is the loss of regularity of the particle density caused by the the self-excitation of the system. In particular, while initially the evolution of the system can be captured by a suitable Stefan problem, the following irregular behavior necessitates a more robust probabilistic approach. Based on joint work with Sergey Nadtochiy.

• Friday, April 27, 2018, 9:00am, Physics 128, The Fourth Duke Mathematical Journal Conference
  The Fourth Duke Mathematical Journal Conference
  Various

   

  The talks will cover an array of subject areas that are well-represented in the Duke Journal. There will be nine talks by young mathematicians. These speakers are: Emmanuel Breuillard (Munster) Ivan Corwin (Columbia) Alessio Figalli (Zurich) John Pardon (Princeton) Lu Wang (Wisconsin) Melanie Matchett Wood (Wisconsin) Giulia Saccà (MIT) Alex Wright (Stanford) Zhiwei Yun (Yale)

• Saturday, April 28, 2018, 9:00am, Physics 128, The Fourth Duke Mathematical Journal Conference
  The Fourth Duke Mathematical Journal Conference
  Various

   

  The talks will cover an array of subject areas that are well-represented in the Duke Journal. There will be nine talks by young mathematicians. These speakers are: Emmanuel Breuillard (Munster) Ivan Corwin (Columbia) Alessio Figalli (Zurich) John Pardon (Princeton) Lu Wang (Wisconsin) Melanie Matchett Wood (Wisconsin) Giulia Saccà (MIT) Alex Wright (Stanford) Zhiwei Yun (Yale)

• Sunday, April 29, 2018, 9:00am, Physics 128, The Fourth Duke Mathematical Journal Conference
  The Fourth Duke Mathematical Journal Conference
  Various

   

  The talks will cover an array of subject areas that are well-represented in the Duke Journal. There will be nine talks by young mathematicians. These speakers are: Emmanuel Breuillard (Munster) Ivan Corwin (Columbia) Alessio Figalli (Zurich) John Pardon (Princeton) Lu Wang (Wisconsin) Melanie Matchett Wood (Wisconsin) Giulia Saccà (MIT) Alex Wright (Stanford) Zhiwei Yun (Yale)

• Monday, May 14, 2018, 8:00pm, none, Southeastern Probability Conference
  Day 1
  TBA

   

  See https://services.math.duke.edu/~rtd/SEPC2018/SEPC2018.html

• Tuesday, May 15, 2018, 8:00pm, none, Southeastern Probability Conference
  Day 2, ends at noon
  TBA

   

  See https://services.math.duke.edu/~rtd/SEPC2018/SEPC2018.html