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Title:ÌýAn Introduction to the Circuits of Polyhedra, The Circuit Diameter, and Their Applications

Abstract:

The combinatorial diameter of a polyhedron P is the maximum value of a shortest path between two vertices of P, where the path moves along edges of P. Its study is motivated largely by its implications on the running time of the Simplex algorithm.

Title:ÌýParallel strategies for SIDH: towards computing SIDH twice as fast

Abstrtact:

Over the last ten years, there has been an intense research effort to find hard mathematical problems that would be presumably hard to solve by a quantum attacker and at the same time could be used to build reasonably efficient public-key cryptoschemes.

Title:ÌýIntroduction to Monotone Operators

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This talk will be an entry level introduction to the theory of monotone operators as they are presented in Bauschke and Combette’s Convex Analysis and Monotone Operator Theory in Hilbert Spaces.

Title:ÌýVertex-minors and sparsity

Abstract:

We discuss an ongoing project with Jim Geelen and Paul Wollan to describe the structure of graph classes excluding a vertex-minor.

Title:ÌýStrongly cospectralÌývertices in cubelike graphs

Abstract:

A cubelike graph is a CayleyÌýgraph of the elementary abelian 2-group. Two vertices in a graph are strongly copsectral if they are cospectral and parallel.

°Õ¾±³Ù±ô±ð:ÌýCombinatorial Hall algebras

Abstract:

The Hall algebra of a finitary category is an associative (and sometimes Hopf) algebra whose structure constants count the number of extensions between objects.

Title:ÌýRecognizing slack matrices

Abstract:

This week, we will be discussing the topic of slack matrices. Slack matrices arise in the context of lifts of polytopes, where, given a polytope P, we can characterize the existence of a lift of P of a given size in terms of properties of an associated slack matrix.

Title:ÌýBinary Submatroids

Abstract:

A binary matroid can be thought of as a set of nonzero binary vectors.

Title:ÌýRectangular Catalan Algebraic Combinatorics

Abstract:

The enumeration of Dyck-like lattice paths in a m x n rectangle has a long and fruitful history culminating in Bizley-Grossman’s formula (1954). We will discuss how it is natural to extend this formula to weighted enumeration, with parameters accounting for such statistics as area; and to consider parking-function analogs.

Title:ÌýProof of the monotone column permanent conjecture

Abstract:Ìý

In 1993, Jim Haglund conjectured the following.Ìý IfÌý AÌý is aÌý square matrix of real numbers which are weakly decreasing down each column, and J is the all-ones matrix of the same size, then the permanent of the matrix xJ+A is a polynomial with only real roots.