Events

Title: An Efficient Algorithm for Deciding the Vanishing of Schubert Polynomial Coefficients

Abstract:

 Schubert polynomials form a basis of all polynomials and appear in the study of cohomology rings of flag manifolds. The vanishing problem for Schubert polynomials asks if a coefficient of a Schubert polynomial is zero. We give a tableau criterion to solve this problem, from which we deduce the first polynomial time algorithm. These results are obtained from new characterizations of the Schubitope, a generalization of the permutahedron defined for any subset of the n x n grid. In contrast, we show that computing these coefficients explicitly is #P-complete. This is joint work with Anshul Adve and Alexander Yong.

Title: Why are Hoffman's bounds for alpha and chi truly duals of each other?

Abstract:

Two of the most well known eigenvalue bounds for graph parameters look suspiciously related. Our goal in this talk is to confirm this suspicion by casting these bounds into a framework of semidefinite optimization that will give us almost for free a duality relation. As one should always expect in this context, we will see a connection to the Lovász theta function of a graph.

Title: A combinatorial approach to Minkowski tensors of polytopes

Abstract:

Intrinsic volumes of a convex body provide scalar data (volume, surface area, Euler characteristic, etc. ) about the geometry of a convex body independent of the ambient space. Minkowski tensors are the tensor-valued generalization of intrinsic volumes. They provide more complex geometric information about a convex body, such as its shape, orientation, and more.

Title: A tale of two integrals

Abstract:

The Harish-Chandra/Itzykson-Zuber (HCIZ) and Brezin-Gross-Witten (BGW) integrals are a pair matrix integrals which play a prominent role in quantum field theory. Remarkably, these ubiquitous special functions are also significant from the perspective of algebraic combinatorics: they are generating functions for certain classes of Hurwitz numbers.

Title: Feynman integrals as algebraic graph theory

Abstract:

I will overview how Feynman integrals should feel very familiar to algebraic graph theorists, and then say a few words about current directions of interest to me, particularly the c_2 invariant.

Title: Algebraic structure of the Hopf algebra of double posets

Abstract:

A Hopf algebra of double posets was introduced by Claudia Malvenuto and Christophe Reutenauer in 2011, motivated by the study of pictures of tableaux as defined by Zelevinsky. Starting from the correspondence between top-cones in the braid arrangement and partial orders, we investigate several properties of the Hopf algebra of double posets as the image of a Hopf monoid (via the Fock functor). In particular, we obtain a non-cancellative formula for the antipode. A description of the primitive space is also discussed.

Title: A proof of the Erdős–Faber–Lovász conjecture

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.

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

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.