Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
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Friday, December 11, 2020 — 3:30 PM EST
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
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
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
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
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.