Department of Mathematics, Summer_2017
https://services.math.duke.edu/mcal?listgroup-0
Department of Mathematics Upcoming Seminarsen-us2024-03-28T14:41:54-04:00https://services.math.duke.edu/mcal2024-01-01T12:00:00-05:002dailyDirected preferential attachment networks
https://services.math.duke.edu/mcal?abstract-10070
The original preferential attachment model for an undirected network was 10 years ago generalized to a directed network model, where nodes together with out- (in-) directed edges appear sequentially, and where the probability to attach to a given node is proportional to the in- (out-) degree of that node. The bivariate degree distribution is defined as the in- and out-degree of a randomly selected node. In the talk we analyse the model using a new approach where it is shown that the distribution can be characterized by two independent birth processes observed at a common exponentially distributed time-point. The method is easily extended to more realistic models allowing for doubly-directed edges as well as attachment probabilities depending both on in- and out-degree.Tom Britton 2017-06-15T16:00:00-04:0010070probabilityProbability SeminarThu, 15 Jun 2017 17:00:00 EDT119 PhysicsSummer, 2017Thu, 15 Jun 2017 16:00:00 EDTThursday, June 15, 2017, 4:00pmSWIM 2017 Seminar
https://services.math.duke.edu/mcal?abstract-10071
<a href="https://sites.duke.edu/dmj2018/">Various</a> 2017-06-29T09:00:00-04:0010071Other Meetings and EventsSWIM 2017 SeminarSummer, 2017Physics 119Thu, 29 Jun 2017 11:00:00 EDTThursday, June 29, 2017, 9:00amThu, 29 Jun 2017 09:00:00 EDTOn Betti Numbers, Persistence Diagrams, and Minimal Spanning Acycles of Random Complexes
https://services.math.duke.edu/mcal?abstract-10073
A simplicial complex generalizes a graph; it is a collection
of subsets of a vertex set, which is closed under subset operation.
Betti numbers and Persistence Diagram (PD) are topological descriptors
of a simplicial complex; while Betti numbers count holes of different
dimensions, PD tracks the birth and death instances of distinct
topological features as the complex is sequentially built piece by
piece. Separately, a Minimal Spanning Acycle (MSA) generalizes the
notion of a minimal spanning tree to weighted simplicial complexes.
This talk has four parts. In the first part, we shall briefly look at
relevant notions from simplicial homology. In the second part, we will
consider a time varying analogue of the Erdos-Renyi graph, which we
refer to as the dynamic Erdos-Renyi graph. We shall prove that under
suitable assumptions, scaled Betti numbers of this dynamic complex
converge to the stationary Ornstein-Uhlenbeck process as the number of
vertices tends to infinity. In the third part, we shall study the
relationship between a MSA of a weighted simplicial complex and the
associated PD. Using this, we will prove that the extremal weights in
the MSA of a randomly weighted complex and extremal death times in the
associated PD converge to a Poisson point process as the number of
vertices go to infinity. In fact, we shall show that these results
also hold if the random weights have small perturbations. In the
fourth part, we shall look at Cech complexes on the excursion set of a
random Gaussian field, whose covariance satisfies some local and decay
rate conditions. We shall see the precise rate at which the window
size and excursion level should grow to infinity so that,
asymptotically, the different Betti numbers have a Poisson limit. We
shall end with some future directions.Gugan Thoppe (Technion - Israel Institute of Technology)2017-07-21T15:30:00-04:0010073probabilityProbability SeminarFri, 21 Jul 2017 16:30:00 EDT119 PhysicsSummer, 2017Fri, 21 Jul 2017 15:30:00 EDTFriday, July 21, 2017, 3:30pmDepartment [DELETED]
https://services.math.duke.edu/mcal?abstract-12979
Dept. Faculty Meeting 2024-03-22T10:30:00-04:0012979Department of MathematicsR.BryantSpring, 2024Physics 119Fri, 22 Mar 2024 11:30:00 EDTdeletedFriday, March 22, 2024, 10:30amFri, 22 Mar 2024 10:30:00 EDTTBA [DELETED]
https://services.math.duke.edu/mcal?abstract-12849
<a href="https://www.ihes.fr/~urbanik/">David Urbanik</a> (IHES)2024-03-29T13:30:00-04:0012849algebraic geometryAlgebraic Geometry SeminarFriday, March 29, 2024, 1:30pmFri, 29 Mar 2024 13:30:00 EDTZoom linkSpring, 2024Fri, 29 Mar 2024 14:30:00 EDTdeletedTBA [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 SeminarWed, 10 Apr 2024 15:15:00 EDTdeletedPhysics 119Spring, 2024Wed, 10 Apr 2024 15:15:00 EDTWednesday, April 10, 2024, 3:15pmIntTBA [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 SeminarTue, 23 Apr 2024 15:15:00 EDTTuesday, April 23, 2024, 3:15pmdeletedTue, 23 Apr 2024 16:15:00 EDTPhysics 119Spring, 2024 [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 EDTSaturday, May 11, 2024, 11:00amSat, 11 May 2024 14:00:00 EDTdeletedOnsiteSpring, 2024