# Events - September 2022

Friday, September 30, 2022 — 3:30 PM EDT

## Tutte Colloquium - Penny Haxell

Title: The Integrality Gap for the Santa Claus Problem

 Speaker: Penny Haxell Affiliation: University of Waterloo Location: MC 5501 or contact Melissa Cambridge for Zoom link

Abstract:

In the max-min allocation problem, a set of players are to be allocated disjoint subsets of a set of   indivisible resources, such that the minimum utility among all players is maximized.  In the restricted variant, also known as the Santa Claus Problem,  each resource (toy'') has an intrinsic positive value, and each player (child'') covets a subset of the resources. Thus Santa wants to distribute the toys amongst the children, while (to satisfy
jealous parents?) wishing to maximize the minimum total value of toys received by each child. This problem turns out to have a natural reformulation in terms of hypergraph matching.

Friday, September 30, 2022 — 12:00 PM EDT

## Combinatorial Optimization Reading Group - David Kalichman

Title: Stochastic Probing with Applications

 Speaker: David Kalichman Affiliation: University of Waterloo Location: MC 6029 or contact Rian Neogi for the Zoom link

Abstract: We will explore a stochastic probing problem. Given a set of elements which have weights and independent probabilities of being "active," the goal is to construct a subset of active elements of maximum weight. To form such a set, we must "probe" elements sequentially to determine whether they are active.

Monday, September 26, 2022 — 11:30 AM EDT

## Algebraic Graph Theory Seminar - Dave Witte Morris

Title: Automorphisms of direct products of some circulant graphs

 Speaker: Dave Witte Morris Affiliation: University of Lethbridge Location: contact Sabrina Lato for Zoom link

Abstract: The direct product of two graphs X and Y is denoted X x Y. Its automorphism group contains a copy of the direct product of Aut(X) and Aut(Y), but it is not known when this inclusion is an equality, even for the special case where X is a circulant graph and Y = K_2 is a connected graph with only 2 vertices.

Friday, September 23, 2022 — 3:30 PM EDT

## Tutte Colloquium - Levent Tuncel

TItle: A perfect graph, a sparse, symmetric matrix and a homogeneous cone walk into a bar … together??

 Speaker: Levent Tuncel Affiliation: University of Waterloo Location: MC 5501

Abstract:  The talk title above sounds like the beginning of a corny joke; however, in this talk, we will indeed utilize results from a very large number of research areas. Many of these research areas are directly within Combinatorics and Optimization and some are from other areas covered in the rest of the Faculty of Mathematics.

Friday, September 23, 2022 — 12:00 PM EDT

## Combinatorial Optimization Reading Group - Paul Lawrence

Title: On the Adaptivity Gap of Stochastic Orienteering

Abstract: This talk highlights the stochastic orienteering problem, in which we are given a budget B and a graph G=(V,E) with edge distances d(u,v) and a starting vertex x. Each vertex v represents a job with a deterministic reward and a random processing time, drawn from a known distribution.

Thursday, September 22, 2022 — 11:30 AM EDT

## Algebraic Graph Theory Webnotice

Title: Graphical Designs and Gale Duality

Monday, September 19, 2022 — 11:30 AM EDT

## Algebraic Graph Theory Seminar - Qianqian Yang

Title: Essential Covers of the Cube by Hyperplanes

 Speaker: Igor Araujo Affiliation: University of Illinois Urbana-Champaign Location: contact Sabrina Lato for Zoom link

Abstract:  An essential cover of the vertices of the n-cube $\{0,1\}^n$ by hyperplanes is a minimal covering where no hyperplane is redundant, and every variable appears in the equation of at least one hyperplane. Linial and Radhakrishnan gave a construction of an essential cover with $\lceil \frac{n}{2} \rceil + 1$ hyperplanes and showed that $\Omega(\sqrt{n})$ hyperplanes are required.

Friday, September 16, 2022 — 3:30 PM EDT

## Tutte Colloquium - Lap Chi Lau

Title: Cheeger Inequalities for Vertex Expansion and Reweighted Eigenvalues

 Speaker: Lap Chi Lau Affiliation: University of Waterloo Location: MC 5501

Abstract:

The classical Cheeger's inequality relates the edge conductance $\phi$ of a graph and the second smallest eigenvalue $\lambda_2$ of the Laplacian matrix. Recently, Olesker-Taylor and Zanetti discovered a Cheeger-type inequality $\psi^2 / \log |V| \lesssim \lambda_2^* \lesssim \psi$ connecting the vertex expansion $\psi$ of a graph $G=(V,E)$ and the maximum reweighted second smallest eigenvalue $\lambda_2^*$ of the Laplacian matrix. In this work, we first improve their result to $\psi^2 / \log d \lesssim \lambda_2^* \lesssim \psi$ where $d$ is the maximum degree in $G$, which is optimal assuming the small-set expansion conjecture. Also, the improved result holds for weighted vertex expansion, answering an open question by Olesker-Taylor and Zanetti.

Friday, September 16, 2022 — 1:00 PM EDT

## Combinatorial Optimization Reading Group - David Kalichman

Title: Stochastic Probing with Applications

 Speaker: David Kalichman Affiliation: University of Waterloo Location: MC 6029 or contact Rian Neogi for Zoom link

Abstract:  We will explore a stochastic probing problem. Given a set of elements which have weights and independent probabilities of being "active," the goal is to construct a subset of active elements of maximum weight. To form such a set, we must "probe" elements sequentially to determine whether they are active.

Monday, September 12, 2022 — 8:00 PM EDT

## Algebraic Graph Theory Seminar - Qianqian Yang

Title: On sesqui-regular graphs with fixed smallest eigenvalue

 Speaker: Qianqian Yang Affiliation: Shanghai University Location: Contact Sabrina Lato for Zoom link

Abstract: Let λ ≥ 2 be an integer. For strongly regular graphs with parameters (v, k, a, c) and fixed smallest eigenvalue −λ, Neumaier gave two bounds on c by using algebraic property of strongly regular graphs. Subsequently, we studied a new class of regular graphs called sesqui-regular graphs, which contains strongly regular graphs as a subclass, and proved that for a given sesqui-regular graph with parameters (v, k, c) and smallest eigenvalue −λ, if k is very large, then either c ≤ λ² (λ − 1) or v − k − 1 ≤ (λ−1)²/4 + 1. This is joint work with Jack Koolen, Brhane Gebremichel and Jae Young Yang

Friday, September 9, 2022 — 1:00 PM EDT

## Combinatorial Optimization Reading Group - Nathan Benedetto

Title: Conditional Value-at-Risk

 Speaker: Nathan Benedetto Affiliation: University of Waterloo Location: MC 6029 or contact Rian Neogi for the Zoom link

Abstract: The mean and variance of a probability distribution may not reflect what one wants from a scenario involving uncertainty.In particular, such measures fall short of expressing risk in a way suitable for financial and similar applications.

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