Seminar

Title: An equivariant basis for the cohomology of Springer fibers

Abstract:

Springer fibers are subvarieties of the flag variety that play an important role in combinatorics and geometric representation theory. In this talk, I will discuss joint work with Martha Precup where we analyze the equivariant cohomology of Springer fibers in type A.

Title: Triangle-free Strongly Regular Graphs

Abstract:

Complete bipartite graphs aside, only five triangle-free strongly regular graphs are known. I will describe some of the background to this topic, with the focus on outlining the construction of the Higman-Sims graph.

Title: Parallel 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: A generalization of balanced tableaux and matching problems with unique solutions

Abstract:

In this talk, we consider families of finite sets that we call shellable and that have been characterized by Chang and Hirst and Hughes as being the families of sets that admit unique solutions to Hall's matching problem.

Title: Moore Graphs

Abstract:

Moore graphs were introduced by Hoffman and Singleton in a fundamental paper. They can be defined as graphs with diameter $d$ and girth $2d+1$.

Title: List Colouring and Ohba's Conjecture

Abstract:

The question of when the list-chromatic number of a graph G, denoted chi_l(G), equals its chromatic number is fundamental to the theory of list colouring.

Title: The Aggregation Closure is Polyhedral for Packing and Covering Integer Programs

Abstract:

Recently, Bodur, Del Pia, Dey, Molinaro and Pokutta introduced the concept of aggregation cuts for packing and covering integer programs.

Title: An 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: Minimum degree conditions for Hamilton cycles in hypergrahs

Abstract:

A classic result of Dirac states that a graph in which every vertex is connected to at least half of the other vertices contains a Hamilton cycle. How can we generalize Dirac's theorem to hypergraphs?

Title: Random Pattern-Avoiding Permutations

Abstract:

A "pattern of length k" is simply a permutation of {1,..,k}.  This pattern is said to be contained in a permutation of {1,...,N} (for N>k) if there is a subsequence of k elements of the (long) permutation that appears in the same relative order as the pattern.