July 2022

Monday, July 4, 2022 — 11:30 to 11:30 AM EDT

Title: Spectral Turan Problems on trees and even cycles

Speaker: Dheer Noal Affiliation: University of Delaware Zoom: Please contact Sabrina Lato for Zoom link

Abstract:  In this talk, we discuss some recent progress with the spectral analogue of a few Turán problems: Instead of maximizing the number of edges, our objective is to maximize the spectral radius of the adjacency matrices of graphs not containing some subgraphs.

Tuesday, July 5, 2022 — 2:30 PM EDT

Title: Bounded treewidth in hereditary graph classes

Speaker: Sepehr Hajebi Affiliation: University of Waterloo Location: MC 5417

Abstract: A highlight of the superb graph minors project of Robertson and Seymour is their so-called Grid Theorem: a minor-closed class of graphs has bounded treewidth if and only it does not contain all planar graphs. Which induced-subgraph-closed graph classes have bounded treewidth?

Thursday, July 7, 2022 — 1:00 PM EDT

Title: Box-ball systems, RSK, and Motzkin paths 

Speaker: Emily Gunawan Affiliation: University of Oklahoma Location: MC 5479, please contact Olya Mandelshtam for Zoom link.

Abstract:  A box-ball system (BBS) is a discrete dynamical system whose dynamics come from the balls jumping according to certain rules. A permutation on n objects gives a BBS state by assigning its one-line notation to n consecutive boxes. After a finite number of steps, a box-ball system will reach a steady state. From any steady state, we can construct a tableau called the soliton decomposition of the box-ball system.

Friday, July 8, 2022 — 1:00 PM EDT

Title: Stochastic Optimization

Speaker: Ricardo Fukasawa Affiliation: University of Waterloo Location: MC 6029

Abstract: While deterministic optimization problems are very useful in practice, often times the assumption that all data is known in advance does not hold true. One possible way to relax this assumption is to assume that the data depends on random variables. This assumption leads to stochastic optimization problems.

Friday, July 8, 2022 — 3:30 PM EDT

Title: 3-colouring via flows

Speaker: Ben Moore Affiliation: Charles University Location: MC 5501 or please contact Melissa Cambridge for Zoom link

Abstract: I'll show a technique to colour graphs on surfaces using max-flow min-cut.

Monday, July 11, 2022 — 11:30 to 11:30 AM EDT

Title: Strong Cospectrality in Trees

Tuesday, July 12, 2022 — 2:30 PM EDT

Title: The k-independence number of graph products

Speaker: Hidde Koerts Affiliation: University of Waterloo Location: MC 5417

Abstract: The k-independence number of a graph is the maximum size of a set of vertices at pairwise distance greater than k, generalizing the standard independence number. In this talk, I will discuss well-known sharp bounds on the independence number of graph products, and extend some of these bounds to the k-independence number. Specifically, we will cover the Cartesian, tensor, strong, and lexicographic products.

Joint work with Aida Abiad.

Thursday, July 14, 2022 — 1:00 PM EDT

Title: An identity in the group algebra of the symmetric group

Speaker: Kevin Purbhoo Affiliation: University of Waterloo Location: MC 5479, contact Olya Mandelshtam for Zoom link

Abstract: Come with me on a magical journey into the mysterious world of inverse Wronskians.

Friday, July 15, 2022 — 1:00 PM EDT

Title: Stochastic Optimization

Speaker: Ricardo Fukaswaw Affiliation: University of Waterloo Location MC 6029 or please contact Rian Neogi for Zoom link

Abstract:  While deterministic optimization problems are very useful in practice, often times the assumption that all data is known in advance does not hold true. One possible way to relax this assumption is to assume that the data depends on random variables.

Friday, July 15, 2022 — 3:30 PM EDT

Title: Positivity and sums of squares in products of free algebras

Speaker: William Slofstra Affiliation: University of Waterloo Location MC 5501 or please contact Melissa Cambridge for Zoom link

Abstract: A noncommutative polynomial is said to be positive relative to some constraints if plugging matrices (or more generally, operators on a Hilbert space) satisfying the constraints into the polynomial always yields a positive operator. It is a natural problem to determine whether or not a given polynomial is positive, and if it is, to find some certificate of positivity. This problem is closely connected with noncommutative polynomial optimization, where we want to find matrices or operators that maximize the operator norm of some polynomial, subject to the constraint that some other polynomials in the operators are positive or vanish. When the algebra cut out by the constraints is a free algebra, free group algebra, or similar algebra, it's well-known that a polynomial is positive on operators satisfying the constraints if and only if it's a sum of Hermitian squares in the algebra.

Monday, July 18, 2022 — 11:30 to 11:30 AM EDT

Title: New Characterizations of Distance-Biregular Graphs

Speaker: Sabrina Lato Affiliation: University of Waterloo Location: please contact Sabrina Lato for Zoom link

Abstract: Fiol, Garriga, and Yebra introduced the notion of pseudo-distance-regular vertices, and were able to use this notion to come up with a characterization of when a graph is distance-regular. Subsequently, Fiol and Garriga were able to use pseudo-distance-regular vertices and a bound on the excess of a vertex to come up with another characterization of distance-regular graphs. We will present an overview of their results, as well as recent extensions to distance-biregular graphs.

Tuesday, July 19, 2022 — 2:30 PM EDT

Title: High-Rank Matroids and Unavoidable Flats

Speaker: Matt Kroeker Affiliation: University of Waterloo Location: MC 5417

Abstract: We discuss a variety of questions and results pertaining to conjectures of Geelen from 2021 on the unavoidable flats in matroids of sufficiently high rank. We will also explore the differences in how such questions are posed for various classes of matroids, why such differences are necessary, and how they could potentially be reconciled. A result for the class of binary matroids and an outline of its proof will be discussed in detail. Joint work with Jim Geelen.

Friday, July 22, 2022 — 1:00 PM EDT

Title: Data-Driven Chance Constrained Programs over Wasserstein Balls

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

Abstract: In many real-world applications, precise problem data is not available to the decision maker. One way to handle this uncertainty is by using chance-constraints, where the probability that at least one constraint is violated is bounded above by some parameter. However, such an approach assumes that the decision maker has access to the true probability distribution which governs the data behavior.

Friday, July 22, 2022 — 3:30 PM EDT

Title: Strongly regular graphs with a regular point 

Speaker: Krystal Guo Affiliation: University of Amsterdam, Korteweg-de Vries Institute  Location MC 5501 or please contact Melissa Cambridge for the Zoom link

Abstract:  Arising from Hoffman and Singleton's study of Moore graphs, strongly regular graphs play an important role in algebraic graph theory. Strongly regular graphs can be construct from geometric objects, such as generalized quadrangles and certain geometric properties, such as having a regular point, can be studied in the context of graphs.

Thursday, July 28, 2022 — 1:00 PM EDT

Title: Thresholds

Speaker: Jinyoung Park Affiliation: Standford University Location: Please contact Logan Crew for the Zoom link

Abstract: Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas. In 2006, Kahn and Kalai conjectured that for any nontrivial increasing property on a finite set, its threshold is never far from its "expectation-threshold," which is a natural (and often easy to calculate) lower bound on the threshold. In this talk, I will present recent progress on this topic. Based on joint work with Huy Tuan Pham.

Friday, July 29, 2022 — 1:00 PM EDT

Title: Stochastic Load Balancing on Unrelated Machines

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

Abstract: We will take a look at the stochastic load balancing problem. The goal is to assign tasks to machines, so that the maximum amount of time taken by any machine to complete all its assigned tasks is minimized. The stochastic twist to this problem is that now the time required to complete each task is a random variable sampled from some known distribution. For the stochastic version, we need to minimize the maximum time taken by any machine in expectation. We will look at a constant factor approximation algorithm for this problem that appeared in a recent paper by Gupta, Kumar, Nagarajan and Shen.

Friday, July 29, 2022 — 3:30 PM EDT

Title: Non-realizability of polytopes via linear programming

Speaker: Amy Wiebe Affiliation: UBC Okanagan Location: MC 5501 or contact Melissa Cambridge for Zoom link

Abstract: A classical question in polytope theory is whether an abstract polytope can be realized as a concrete convex object. Beyond dimension 3, there seems to be no concise answer to this question in general. In specific instances, answering the question in the negative is often done via “final polynomials” introduced by Bokowski and Sturmfels. This method involves finding a polynomial which, based on the structure of a polytope if realizable, must be simultaneously zero and positive, a clear contradiction.

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