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Tuesday, July 12, 2022 2:30 pm - 2:30 pm EDT (GMT -04:00)

Graph and Matroids Seminar - Hidde Koert

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 - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Kevin Purbhoo

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 - 1:00 pm EDT (GMT -04:00)

Combinatorial Optimization Reading Group - Ricardo Fukasawa

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 - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - William Slofstra

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 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Sabrina Lato

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 - 2:30 pm EDT (GMT -04:00)

Graph and Matroids Seminar - Matt Kroeker

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 - 1:00 pm EDT (GMT -04:00)

Combinatorial Optimization Reading Group - Matheus Ota

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 - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Krystal Guo

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.