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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.

Friday, December 4, 2020 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Oliver Pechenik

Title: Partial orders on the symmetric group

Speaker: Oliver Pechenik
Affiliation: University of Waterloo
Zoom: Please email Emma Watson

Abstract:

The symmetric group of permutations is naturally a poset in at least 4 different ways, the (strong) Bruhat order and three flavors of weak order. Stanley showed in 1980 that the Bruhat order is Sperner, essentially meaning that the obvious large antichains are in fact the largest possible. The corresponding fact for weak orders was open until last year, when it was established by Gaetz and Gao.

Monday, December 7, 2020 11:30 am - 11:30 am EST (GMT -05:00)

Algebraic Graph Theory Seminar - Shahla Nasserasr

Title: Distinct Eignvalues and Sensitivity

Speaker: Shahla Nasserasr
Affiliation: Rochester Institute of Technology
Zoom: Contact Soffia Arnadottir

Abstract: 

For a graph $G$, the class of real-valued symmetric matrices whose zero-nonzero pattern of off-diagonal entries is described by the adjacencies in $G$ is denoted by $S(G)$. The inverse eigenvalue problem for the multiplicities of the eigenvalues of $G$ is to determine for which ordered list of positive integers $m_1\geq m_2\geq \cdots\geq m_k$ with $\sum_{i=1}^{k} m_i=|V(G)|$, there exists a matrix in $S(G)$ with distinct eigenvalues ${\lambda_1,\lambda_2,\cdots, \lambda_k}$ such that $\lambda_i$ has multiplicity $m_i$.