10/5/2021 Combinatorics, Physics and Probability Seminar
Title: Geodesic Geometry on Graphs Abstract: In a graph G = (V, E) we consider a system of paths S so that for every two vertices u,v in V there is a […]
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10/12/2021 Combinatorics, Physics and Probability Seminar
Title: On counting algebraically defined graphs Abstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane), the edges of […]
10/19/2021 Combinatorics, Physics and Probability Seminar
Title: Ising model, total positivity, and criticality Abstract: The Ising model, introduced in 1920, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical […]
The n-queens problem
Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another, and the […]
Prague dimension of random graphs
Abstract: The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity, it is closely related to clique edges coverings […]
Resistance curvature – a new discrete curvature on graphs
Abstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential […]
The singularity probability of random symmetric matrices
Abstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1,1}. In this talk I’ll consider the following basic question: what is the probability that […]
The longest induced path in a sparse random graph
Abstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from […]
Adventures in Perturbation Theory
Abstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of […]
The Amplituhedron BCFW Triangulation
Abstract: The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the […]
Invariant theory for maximum likelihood estimation
Abstract: I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum […]
Equiangular lines and regular graphs
Abstract: In 1973, Lemmens and Seidel asked to determine N_alpha(r), the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently, this problem has been almost completely settled when […]