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Please note: The University of Waterloo is closed for all events until further notice.

# Events - December 2020

Friday, December 11, 2020 — 3:30 PM EST

## Tutte Colloquium - Santanu Dey

Title: Sparse PSD approximation of the PSD cone

 Speaker: Santanu Dey Affiliation: H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology Zoom: Please email Emma Watson

Abstract:

While semidefinite programming (SDP) problems are polynomially solvable in theory, it is often difficult to solve large SDP instances in practice. One computational technique used to address this issue is to relax the global positive-semidefiniteness (PSD) constraint and only enforce PSD-ness on smaller k × k principal submatrices — we call this the sparse SDP relaxation.

Thursday, December 10, 2020 — 1:00 PM EST

## Algebraic Combinatorics Seminar - Laura Colmenarejo

Title: Chromatic symmetric functions of Dyck paths and $q$-rook theory

 Speaker: Laura Colmenarejo Affiliation: UMass Amherst Zoom: Contact Karen Yeats

Abstract:

Given a graph and a set of colors, a coloring of the graph is a function that associates each vertex in the graph with a color. In 1995, Stanley generalized this definition to symmetric functions by looking at the number of times each color is used and extending the set of colors to $\mathbb{Z}^+$. In 2012, Shareshian and Wachs introduced a refinement of the chromatic functions for ordered graphs as $q$-analogues.

Monday, December 7, 2020 — 11:30 AM EST

## 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 $m_i$.

Friday, December 4, 2020 — 3:30 PM EST

## 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.

Thursday, December 3, 2020 — 1:00 PM EST

## 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.

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