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 […]
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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 […]
Rational Polypols
Abstract: Eugene Wachspress introduced polypols as real bounded semialgebraic sets in the plane that generalize polygons. He aimed to generalize barycentric coordinates from triangles to arbitrary polygons and further to […]
Greedy maximal independent sets via local limits
Abstract: The random greedy algorithm for finding a maximal independent set in a graph has been studied extensively in various settings in combinatorics, probability, computer science, and chemistry. The algorithm builds […]
Moduli space of tropical curves, graph Laplacians and physics
Abstract: I will first review the construction of the moduli space of tropical curves (or metric graphs), and its relation to graph complexes. The graph Laplacian may be interpreted as a […]