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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.

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.

Thursday, November 12, 2020 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Christos Athanasiadis

Title: Face enumeration and real-rootedness

Speaker: Christos Athanasiadis
Affiliation: University of Athens
Zoom: Contact Karen Yeats

Abstract:

About fifteen years ago F. Brenti and V. Welker showed that the face enumerating polynomial of the barycentric subdivision of any Cohen-Macaulay simplicial complex has only real roots. It is natural to ask whether similar results hold when barycentric subdivision is replaced by more general types of triangulations, or when simplicial complexes are replaced by more general cell complexes.

Friday, November 13, 2020 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Nisheeth Vishnoi

Title: Sampling Under Symmetry

Speaker: Nisheeth Vishnoi
Affiliation: Yale University
Zoom: Please email Emma Watson

Abstract:

Exponential densities on orbits of Lie groups such as the unitary group are endowed with surprisingly rich mathematical structure and. traditionally, arise in diverse areas of physics, random matrix theory, and statistics.

In this talk, we will discuss the computational properties of such distributions and also present new applications to quantum inference and differential privacy.

Monday, November 16, 2020 11:30 am - 11:30 am EST (GMT -05:00)

Algebraic Graph Theory Seminar - Xiaohong Zhang

Title: Fractional revival on graphs

Speaker: Xiaohong Zhang
Affiliation: University of Waterloo
Zoom: Contact Soffia Arnadottir

Abstract:

Let A be the adjacency matrix of a weighted graph, and let U(t)=exp(itA). If there is a time t such that U(t)e_a=\alpha e_a+\beta e_b, then we say there is fractional revival (FR) between a and b. For the special case when \alpha=0, we say there is perfect state transfer (PST) between vertices a and b. It is known that PST is monogamous (PST from a to b and PST from a to c implies b=c) and vertices a b are cospectral in this case. If \alpha\beta\neq 0, then there is proper fractional revival.

Thursday, November 19, 2020 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - David Wagner

Title: Some new lemmas about polynomials with only real roots

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

Abstract:

Recent investigations in Ehrhart theory suggested some conjectures involving interlacing relations among polynomials with only real roots, and Veronese sections of them. Revisiting some old theorems, we find as corollaries some new lemmas which have been overlooked for a long time. One of these lemmas directly implies a strong form of the motivating conjecture.  Similar applications of the other lemmas are anticipated. This is ongoing joint work with Christos Athanasiadis (U. Athens).

Friday, November 20, 2020 3:30 pm - 3:30 pm EST (GMT -05:00)

Distinguished Tutte Lecture - Jordan Ellenberg

Jordan Ellenberg Headshot

Title: Beyond rank

Speaker: Jordan Ellenberg
Affiliation: University of Wisconsin
Zoom: Please email Emma Watson

Abstract:

The notion of the rank of a matrix is one of the most fundamental in linear algebra. The analogues of this notion in multilinear algebra — e.g., what is the “rank” of an m x n x p array of numbers? — is much more mysterious, but it also has proven to be useful in a wide array of contexts. I will talk about some questions and answers in “higher rank” coming from complexity theory, data science, geometric combinatorics, additive number theory, and commutative algebra.

Monday, November 23, 2020 11:30 am - 11:30 am EST (GMT -05:00)

Algebraic Graph Theory Seminar - Nathan Lindzey

Title: Complexity Measures on the Symmetric Group and Beyond

Speaker: Nathan Lindzey
Affiliation: CU Boulder
Zoom: Contact Soffia Arnadottir

Abstract:

A classical result in complexity theory states that a degree-d Boolean function on the hypercube can be computed using a decision tree of depth poly(d). Conversely, a Boolean function computed by a decision tree of depth d has degree at most d. Thus degree and decision tree complexity are polynomially related. Many other complexity measures of Boolean functions on the hypercube are polynomially related to the degree (e.g., approximate degree, certificate complexity, block sensitivity), and last year Huang famously added sensitivity to the list. Can we prove similar results for Boolean functions on other combinatorial domains?

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

Algebraic Graph Theory Seminar - Krystal Guo

Title: Simple eigenvalues of graph

Speaker: Krystal Guo
Affiliation: University of Amsterdam
Zoom: Contact Soffia Arnadottir

Abstract:

If v is an eigenvector for eigenvalue λ of a graph X and α is an automorphism of X, then α(v) is also an eigenvector for λ. Thus it is rather exceptional for an eigenvalue of a vertex-transitive graph to be simple. We study cubic vertex-transitive graphs with a non-trivial simple eigenvalue, and discover remarkable connections to arc-transitivity, regular maps and Chebyshev polynomials.

Thursday, December 3, 2020 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Loïc Foissy

Title:Twisted Hopf algebras

Speaker: Loïc Foissy
Affiliation: Université du Côte d'Opale
Zoom: Contact Karen Yeats

Abstract:

A twisted Hopf algebra is a Hopf algebra in the category of linear species. The Fock functors allow to recover "classical" Hopf algebras from twisted ones. Numerous constructions and results can be lifted to the level of twisted bialgebras, such that cofreeness, shuffle and quasi-shuffles products, etc.