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Thursday, March 11, 2021 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Karen Yeats

Title: Equivalences of Wilson loop diagrams

Speaker: Karen Yeats
Affiliation: University of Waterloo
Zoom: Contact Karen Yeats

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.

Friday, March 12, 2021 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Bill Cook

Title: An approximate solution to a 2,079,471-point traveling salesman problem

Speaker: Bill Cook
Affliation: University of Waterloo
Zoom: Please email Emma Watson

Abstract:

Together with Keld Helsguan, we have found a TSP tour through the 3D positions of 2,079,471 stars. We discuss how linear programming allows us to prove the tour is at most a factor of 0.0000074 longer than an optimal solution. The talk will focus on the use of minimum cuts and GF(2) linear systems, to drive the cutting-plane method towards strong LP relaxations.

Monday, March 15, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Willem H. Haemers

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

Speaker: Willem H. Haemers
Affiliation: Tilburg University, Tilburg, The Netherlands
Zoom: Contact Soffia Arnadottir

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.

Thursday, March 18, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - David Wagner

Title: The Poset Conjecture: results, counterexamples, and open problems

Speaker: David Wagner
Affiliation: University of Waterloo
Zoom: Contact Karen Yeats

Abstract:

In 1978, Neggers conjectured that a certain transform of the order polynomial of a partially ordered set (poset) has only real roots.

In the late 1980s, Stanley gave this to me as a thesis project, generalized to labelled posets.  For my thesis I proved the conclusion for series-parallel labelled posets and a bit more.  Br\"and\'en, and later Stembridge, found counterexamples to the conjecture in general.

Friday, March 19, 2021 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Felix Joos

Title: Decompositions of Hypergraphs

Speaker: Felix Joos
Affliation: Heidelberg University
Zoom: Please email Emma Watson

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.

Monday, March 22, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Sarah Plosker

Title: Centrosymmetric Stochastic Matrices

Speaker: Sarah Plosker
Affiliation: Brandon University
Zoom: Contact Soffia Arnadottir

Abstract:

We consider the convex subset of m by n stochastic matrices that are centrosymmetric: stochastic matrices that are symmetric under rotation by 180 degrees. We consider the extreme points and bases of this set, as well as several other parameters associated to such matrices. We provide examples illustrating the results throughout. This is joint work with Lei Cao (Nova Southeastern University) and Darian McLaren (University of Waterloo).

Thursday, March 25, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Colleen Robichaux

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

Speaker: Colleen Robichaux
Affiliation: University of Illinois at Urbana-Champaign
Zoom: Contact Karen Yeats

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.

Monday, March 29, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Gabriel Coutinho

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

Speaker: Gabriel Coutinho
Affiliation: Universidade Federal de Minas Gerais, Brazil
Zoom: Contact Soffia Arnadottir

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.

Thursday, April 1, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Amy Wiebe

Title: A combinatorial approach to Minkowski tensors of polytopes

Speaker: Amy Wiebe
Affiliation: Freie Universität Berlin
Zoom: Contact Karen Yeats

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.

Thursday, April 8, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Jonathan Novak

Title: A tale of two integrals

Speaker: Jonathan Novak
Affiliation: University of California San Diego
Zoom: Contact Karen Yeats

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.