Events - March 2021

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: Decompositions of Hypergraphs

Abstract:

Several results on approximate decompositions of hypergraphs are presented including decompositions into tight Hamilton cycles under very mild assumptions on the host hypergraphs as well as further results on decompositions of quasirandom hypergraphs into bounded degree hypergraphs.

Title: The chromatic index of strongly regular graphs (joint work with Sebastian M. Cioaba and Krystal Guo)

Abstract:

It follows from Vizing's theorem that the chromatic index (edge chromatic number) of a k-regular graph equals k or k+1, and that it equals k+1 if the graph has odd order.

We investigate the chromatic index of strongly regular graphs (SRGs) of even order.

Title: Equivalences of Wilson loop diagrams

Abstract:

I will talk about Wilson loop diagrams, explain a bit about what they are, and some of the combinatorial questions that come out of them, with a focus on when they are equivalent.  This is joint work with Susama Agarwala and Zee Fryer.

Title: The embezzlement of entanglement and its applications

Abstract:

Embezzlement of entanglement is the (impossible) task of producing an entangled state from a product state via a local change of basis, when a suitable *catalytic* entangled state is available.

The possibility to approximate this task was first observed by van Dam and Hayden in 2002.  Since then, the phenomenon is found to play crucial roles in many aspects of quantum information theory.  In this talk, we will discuss aspects of embezzlement and some applications (such as why quantum correlations do not form a closed set, and why there are nonlocal games that cannot be played optimally with a finite amount of entanglement, and why additive quantities cannot be more than asymptotically continuous).

Title: Graphs and combinatorics with a relationship to algebra, geometry and physics

Abstract:

Several algebraic and geometric structures are most naturally encoded via graphs. These include restrictions, such as trees, and decorations, such as planar graphs, ribbon graphs, bi-partite graphs (aka. hypergraphs), directed versions, etc. Particularly nice properties satisfy some kind of hereditary condition. This affords a dual perspective. Either as (nested) subsets and decomposition, or as composition, gluing locally. Both views relate to category theory, algebra, and combinatorics in terms of finite sets, cospans etc. We will give examples of these phenomena and provide a general background.