Events

Title: A Spectral Moore Bound for Bipartite Semiregular Graphs

Abstract:

The Moore bound provides an upper bound on the number of vertices of a regular graph with a given degree and diameter, though there are disappointingly few graphs that achieve this bound. Thus, it is interesting to ask what additional information can be used to give Moore-type bounds that are tight for a larger number of graphs. Cioaba, Koolen, Nozaki, and Vermette considered regular graphs with a given second-largest eigenvalue, and found an upper bound for such graphs.

Title: Quantum independence number

Abstract:

From this talk you will be able to learn what quantum independence number is and how it is different from the classical independence number. I will provide both known individual and infinite families of the graphs where classical and quantum independent numbers are different, as well as some of our generalisations of these examples.  

Title: Interlacing methods in Extremal Combinatorics

Title: Minimum eigenvalue of nonbipartite graphs

Abstract:

Let \rho and \lambda be the largest and the smallest eigenvalue of a connected graph G. It is well-known that \rho + \lambda \geq 0 and that equality occurs if and only if G is bipartite. The speaker will discuss what else can we say when G is not bipartite.

Title: q-Whittaker functions, finite fields, and Jordan forms

Abstract:

The q-Whittaker symmetric function associated to an integer partition is a q-analogue of the Schur symmetric function. We give a new formula for the q-Whittaker function in terms of partial flags compatible with a nilpotent endomorphism over the finite field of size 1/q.

Title: Algebraic formulations of Zauner's conjecture

Title: An algebraic framework for twualities of embedded graphs

Abstract:

We develop algebraic tools to identify and generate new surface embeddings of graphs with various forms of self-twuality including geometric duality, Petrie duality, Wilson duality, and both forms of triality (which is like duality, but of order three instead of two).  These operations are of particular interest because of their interplay with graph symmetries and graph polynomials.

Title: What is the degree of a Grothendieck polynomial?

Abstract:

Jenna Rajchgot observed that the Castelnuovo-Mumford regularity of matrix Schubert varieties is computed by the degrees of the corresponding Grothendieck polynomials. We give a formula for these degrees.

Title: On the approximability of the maximum cardinality stable matching problem with ties