Future students

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: Algebraic formulations of Zauner's conjecture

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: 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: Interlacing methods in Extremal Combinatorics

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: 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: Robust Interior Point Methods for Key Rate Computation in Quantum Key Distribution

Title: Quantum walks on Cayley graphs

Abstract:

In this talk we will look at the continuous-time quantum walk on Cayley graphs of finite groups. We will show that normal Cayley graphs enjoy several nice algebraic properties, and then look at state transfer phenomena in Cayley graphs of certain non-abelian p-groups called the extraspecial p-groups. Some of the results we present are part of joint work with Peter Sin.