Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
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.
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.
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: 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: 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: 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: 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.
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.