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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.

Title:ÌýImproving the general upper bound for Hadwiger's conjecture

Abstract:

In 1943, Hadwiger conjectured that every K_t-minor-free graph has chromatic number at most t-1.

Title:

Abstract:

Differential privacy is about preserving an individuals privacy while maintaining utility in the context of data analysis.

Title:ÌýWidths in even-hole-free graphs

Abstract:

Historically, the study of even-hole-free graphs is motivated by the analogy with perfect graphs. The decomposition theorems that are known for even-hole-free graphsÌýare seemingly more powerful than the ones for perfect graphs: the basic classes and the decompositions are more restricted.