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

Events - October 2020

Friday, October 30, 2020 — 3:30 PM EDT

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.

Friday, October 23, 2020 — 3:30 PM EDT

Title: Semidefinite Programming Relaxations of the Traveling Salesman Problem

Speaker: David P. Williamson
Affiliation: Cornell University
Zoom: Please email Emma Watson

Abstract:

Finding a polynomial-time solvable relaxation of the traveling salesman problem whose integrality gap better matches what is seen in practice has been an outstanding open problem in combinatorial optimization for some time.  We study several semidefinite programming relaxations of the traveling salesman problem proposed in the literature and show that all known relaxations have an unbounded integrality gap.

Thursday, October 22, 2020 — 1:00 PM EDT

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.

Wednesday, October 21, 2020 — 4:30 PM EDT

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.

Monday, October 19, 2020 — 3:00 PM EDT

Title: The Hepp bound of a matroid: flags, volumes and integrals

Speaker: Erik Panzer
Affiliation: University of Oxford
Zoom: Contact Rose McCarty

Abstract:

Invariants of combinatorial structures can be very useful tools that capture some specific characteristics, and repackage them in a meaningful way. For example, the famous Tutte polynomial of a matroid or graph tracks the rank statistics of its submatroids, which has many applications, and relations like contraction-deletion establish a very close connection between the algebraic structure of the invariant (e.g. Tutte polynomials) and the actual matroid itself.

Monday, October 19, 2020 — 11:30 AM EDT

Title: Pretty Good State Transfer and Minimal Polynomials

Speaker: Christopher van Bommel
Affiliation: University of Manitoba
Zoom: Contact Soffia Arnadottir

Abstract:

We examine conditions for a pair of strongly cospectral vertices to have pretty good quantum state transfer in terms of minimal polynomials, and provide cases where pretty good state transfer can be ruled out.

Friday, October 9, 2020 — 3:30 PM EDT

Title: Generalization bounds for rational self-supervised learning algorithms

Speaker: Boaz Barak
Affiliation: Harvard University
Zoom: Please email Emma Watson

Abstract:

The generalization gap of a learning algorithm is the expected difference between its performance on the training data and its performance on fresh unseen test samples.Modern deep learning algorithms typically have large generalization gaps, as they use more parameters than the size of their training set. Moreover the best known rigorous bounds on their generalization gap are often vacuous.

Thursday, October 8, 2020 — 1:00 PM EDT

Title: Factorization problems in complex reflection groups

Speaker: Alejandro Morales
Affiliation: University of Massachusetts Amherst
Zoom: Contact Karen Yeats

Abstract:

The study of factorizations in the symmetric group is related to combinatorial objects like graphs embedded on surfaces and non-crossing partitions. We consider analogues for complex reflections groups of certain factorization problems of permutations first studied by Jackson, Schaeffer, Vassilieva and Bernardi.

Monday, October 5, 2020 — 11:30 AM EDT

Title: Efficient $(j,k)$-Domination

Speaker: Brendan Rooney
Affiliation: Rochester Institute of Technology
Zoom: Contact Soffia Arnadottir

Abstract:

A function $f:V(G)\rightarrow\{0,\ldots,j\}$ is an efficient $(j,k)$-dominating function on $G$ if $\sum_{u\in N[v]}f(u)=k$ for all $v\in V(G)$ (here $N[v]=N(v)\cup\{v\}$ is the closed neighbourhood of $v$).

Friday, October 2, 2020 — 3:30 PM EDT

Title: Total Dual Integrality for Convex, Semidefinite and Extended Formulations

Speaker: Levent Tuncel
Affiliation: University of Waterloo
Zoom: Please email Emma Watson

Abstract:

Within the context of characterizations of exactness of convex relaxations of 0,1 integer programming problems, we present a notion of total dual integrality for Semidefinite Optimization Problems (SDPs), convex optimization problems and extended formulations of convex sets.

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