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Wednesday, October 21, 2020 4:30 pm - 4:30 pm EDT (GMT -04:00)

Joint Colloquium PMath+CO - Nick Olson-Harris

Title: On the Theory of the Analytical Forms called Trees

Speaker: Nick Olson-Harris
Affiliation: University of Waterloo
Zoom: Contact Maxwell Levit

Abstract:

Trees are among the most fundamental of combinatorial structures. Nowadays they appear all over mathematics and computer science, but this has not always been the case. Trees were first introduced, at least under that name, in an 1857 paper of Cayley by the same title as this talk.

Thursday, October 22, 2020 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Reuven Hodges

Title: Coxeter combinatorics and spherical Schubert geometry

Speaker: Reuven Hodges
Affiliation: University of Illinois
Zoom: Contact Karen Yeats

Abstract:

This talk will introduce spherical elements in a finite Coxeter system. These spherical elements are a generalization of Coxeter elements, that conjecturally, for Weyl groups, index Schubert varieties in the flag variety G/B that are spherical for the action of a Levi subgroup.

Monday, October 26, 2020 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Ferdinand Ihringer

Title: Pseuodrandom Cliquefree Graphs, Finite Geometry, and Spectra

Speaker: Ferdinand Ihringer
Affiliation: Ghent University, Belgium
Zoom: Contact Soffia Arnadottir

Abstract:

A regular graph is called optimally pseudorandom if its second largest eigenvalue in absolute value is, up to a constant factor, as small as possible. Determining the largest degree of an optimally pseudorandom graph without a clique of size s is a well-known open problem in extremal graph theory.

Thursday, October 29, 2020 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Florian Aigner

Title: qRSt: A probabilistic Robinson--Schensted correspondence for Macdonald polynomials

Speaker: Florian Aigner
Affiliation: Université du Québec à Montréal
Zoom: Contact Karen Yeats

Abstract:

The Robinson--Schensted (RS) correspondence is a bijection between permutations and pairs of standard Young tableaux which plays a central role in the theory of Schur polynomials. In this talk, I will present a (q,t)-dependent probabilistic deformation of Robinson--Schensted which is related to the Cauchy identity for Macdonald polynomials.

Friday, October 30, 2020 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Logan Crew

Title: The Tutte Symmetric Function

Speaker: Logan Crew
Affiliation: University of Waterloo
Zoom: Please email Emma Watson

Abstract:

The Tutte polynomial is one of the most celebrated and most well-studied graph functions, in part because it specializes to every graph polynomial with a linear deletion-contraction relation, such as the chromatic polynomial. In the 1990s, Stanley generalized the Tutte polynomial to a symmetric function, but at the cost of the deletion-contraction relation.

Monday, November 2, 2020 11:30 am - 11:30 am EST (GMT -05:00)

Algebraic Graph Theory Seminar - Sabrina Lato & Christino Tamon

Title: Monogamy Violations in Perfect State Transfer

Speakers: Sabrina Lato & Christino Tamon
Affiliations: University of Waterloo & Clarkson Unversity
Zoom: Contact Soffia Arnadottir

Abstract:

Continuous-time quantum walks on a graph are defined using a Hermitian matrix associated to a graph. For a quantum walk on a graph using either the adjacency matrix or the Laplacian, there can be perfect state transfer from a vertex to at most one other vertex in the graph.

Thursday, November 5, 2020 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Huda Ahmed and Yuanning Zhang

Title: Filtering Grassmannian cohomology via k-Schur functions

Speakers: Huda Ahmed and Yuanning Zhang
Affiliation: New York University and UC Berkeley
Zoom: Contact Karen Yeats

Abstract:

This talk concerns the cohomology rings of complex Grassmannians. In 2003, Reiner and Tudose conjectured the form of the Hilbert series for certain subalgebras of these cohomology rings. We build on their work in two ways. First, we conjecture two natural bases for these subalgebras that would imply their conjecture using notions from the theory of k-Schur functions. Second we formulate an analogous conjecture for Lagrangian Grassmannians.

Joint work with Michael Feigen, Victor Reiner, and Ajmain Yamin.

Thursday, November 5, 2020 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Jonathan Jedwab

Title: Packings of partial difference sets

Speaker: Jonathan Jedwab
Affiliation: Simon Fraser University
Zoom: Contact Karen Yeats

Abstract:

Partial difference sets are highly structured group subsets that occur in various guises throughout design theory, finite geometry, coding theory, and graph theory. They admit only two possible nontrivial character sums and so are often studied using character theory.

Friday, November 6, 2020 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Chloe Martindale

Title: Constructing broken SIDH parameters: a tale of De Feo, Jao, and Plut's serendipity

Speaker: Chloe Martindale
Affiliation: University of Bristol
Zoom: Please email Emma Watson

Abstract:

This talk is motivated by analyzing the security of the cryptographic key exchange protocol SIDH (Supersingular Isogeny Diffie-Hellman), introduced by 2011 by De Feo, Jao, and Plut. We will first recall some mathematical background as well as the protocol itself. The 'keys' in this protocol are elliptic curves, which are typically described by equations in x and y of the form y^2 = x^3 + ax + b.

Monday, November 9, 2020 8:00 pm - 8:00 pm EST (GMT -05:00)

Algebraic Graph Theory Seminar - Hajime Tanaka

Title: Scaling limits for the Gibbs states on distance-regular graphs with classical parameters

Speaker: Hajime Tanaka
Affiliation: Tohoku University
Zoom: Contact Soffia Arnadottir

Abstract:

Limits of the normalized spectral distributions and other related probability distributions of families of graphs have been studied in the context of quantum probability theory as analogues of the central limit theorem. First I will review some of the previous work by Hora, Obata, and others, focusing on the case of distance-regular graphs, and emphasizing how the theory is related to the Terwilliger algebra.