Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
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Monday, May 31, 2021 — 11:30 AM EDT
Title: An algebraic framework for twualities of embedded graphs
| Speaker: | Jo Ellis-Monaghan |
| Affiliation: | Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam |
| Zoom: | Contact Soffia Arnadottir |
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.
Friday, May 28, 2021 — 3:30 PM EDT
Title: Algebraic formulations of Zauner's conjecture
| Speaker: | Jon Yard |
| Affliliation: | University of Waterloo |
| Zoom: | Contact Emma Watson |
Abstract:
Tight complex projective 2-designs are simultaneously maximal sets of equiangular lines and minimal complex projective 2-designs. In quantum information theory, they define optimal measurements known as SIC-POVMs (Symmetric Informationally Complete Positive Operator-Valued Measures). They are conjectured by Zauner to exist in every dimension, even as specific group orbits.
Friday, May 21, 2021 — 3:30 PM EDT
Title: Positivity Problems for Linear Recurrences
| Speaker: | Steve Melczer |
| Affliliation: | University of Waterloo |
| Zoom: | Contact Emma Watson |
Abstract:
Although sequences satisfying linear recurrence relations have been studied for centuries, and appear as some of the first examples of combinatorial sequences encountered in an introductory combinatorics class, there are natural examples of simply stated problems related to their basic behaviour whose decidability is unknown. In this talk we survey some open computability and complexity questions related to the positivity of linearly recurrent sequences, before examining a new approach to proving positivity using rigorous numerical methods for functions satisfying linear differential equations.
Thursday, May 20, 2021 — 1:00 PM EDT
Title: q-Whittaker functions, finite fields, and Jordan forms
| Speaker: | Steven Karp |
| Affiliation: | UQAM |
| Zoom: | Contact Steve Melczer |
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.
Monday, May 17, 2021 — 11:30 PM EDT
Title: Minimum eigenvalue of nonbipartite graphs
| Speaker: | Bojan Mohar |
| Affiliation: | Simon Fraser University |
| Zoom: | Contact Soffia Arnadottir |
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.
Friday, May 14, 2021 — 3:30 PM EDT
Title: Interlacing methods in Extremal Combinatorics
| Speaker: | Hao Huang |
| Affliliation: | Emory University |
| Zoom: | Contact Emma Watson |
Abstract:
Extremal Combinatorics studies how large or how small a collection of finite objects could be, if it must satisfy certain restrictions. In this talk, we will discuss applications of spectral graph theory, more specifically eigenvalue interlacing, to prove various interesting results in Extremal Combinatorics. We will discuss the Erdos-Ko-Rado Theorem and its degree version, an isodiametric inequality for discrete cubes, and the resolution of a thirty-year-old open problem in Theoretical Computer Science, the Sensitivity Conjecture of Nisan and Szegedy. Several open problems will also be mentioned during this talk.
Monday, May 10, 2021 — 11:30 AM EDT
Title: Quantum independence number
| Speaker: | Mariia Sobchuk |
| Affiliation: | University of Waterloo |
| Zoom: | Contact Soffia Arnadottir |
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.