Events

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

Speaker:	Tom Kelly
Affliliation:	University of Birmingham
Zoom:	Contact Emma Watson

Abstract:

The Erdős–Faber–Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. We prove this conjecture for every sufficiently large $n$. This is joint work with Dong Yeap Kang, Daniela Kühn, Abhishek Methuku, and Deryk Osthus.

Title: Quantum walks on Cayley graphs

Speaker:	Julien Sorci
Affiliation:	University of Florida
Zoom:	Contact Soffia Arnadottir

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

Speaker:	Hao Hu
Affliliation:	University of Waterloo
Zoom:	Contact Emma Watson

Abstract:

We study semidefinite programs for computing the key rate in finite dimensional quantum key distribution (QKD) problems. Through facial reduction, we derive a semidefinite program which is robust and stable in the numerical computation. Our program avoids the difficulties for current algorithms from singularities that arise due to loss of positive definiteness. This allows for the derivation of an efficient Gauss-Newton interior point approach. We provide provable lower and upper bounds for the hard nonlinear semidefinite programming problem.

Title: A Spectral Moore Bound for Bipartite Semiregular Graphs

Speaker:	Sabrina Lato
Affiliation:	University of Waterloo
Zoom:	Contact Soffia Arnadottir

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: 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.

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.

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.

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.

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.

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.

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Tutte Colloquium - Tom Kelly

Algebraic Graph Theory Seminar - Julien Sorci

Tutte Colloquium - Hao Hu

Algebraic Graph Theory Seminar - Sabrina Lato

Algebraic Graph Theory Seminar - Mariia Sobchuk

Tutte Colloquium - Hao Huang

Algebraic Graph Theory Seminar - Bojen Mohar

Algebraic Combinatorics Seminar - Steven Karp

Tutte Colloquium - Steve Melczer

Tutte Colloquium - Jon Yard

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