Events

Title: Spectral Turan Problems on trees and even cycles

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.

Title: Bounded treewidth in hereditary graph classes

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?

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

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.

Title: Stochastic Optimization

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.

Title: 3-colouring via flows

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

Title: Strong Cospectrality in Trees

Title: The k-independence number of graph products

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.

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

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

Title: Stochastic Optimization

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.

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

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.