Events

Title: Stochastic Minimum Norm Combinatorial Optimization

Abstract: In this work, we introduce and study stochastic minimum-norm optimization. We have an underlying combinatorial optimization problem where the costs involved are random variables with given distributions; each feasible solution induces a random multidimensional cost vector. The goal is to find a solution that minimizes the expected norm of the induced cost vector, for a given monotone, symmetric norm.

Title: The ADMM:  Past, Present, and Future

Abstract: Over the past 15 years, the alternating direction method of multipliers (ADMM) has become a standard optimization method.  This talk will cover the origins of the ADMM, its subsequent development, and what to expect in the future.

Title: Cliques in dense matroids

Abstract: We will give a singly exponential bound on the number of points a $U_{2,q+2}$-minor-free matroid can have without containing $M(K_{q+2})$ as a minor.

Title: Equiangular lines and algebraic number theory

Abstract: It is believed that SICs, that is maximal equiangular tight frames, exist in all complex vector spaces. To construct them we use the Weyl-Heisenberg groups, and hence the cyclotomic numbers (roots of unity).

Title: The Hat Guessing Number of Graphs

Abstract:  The hat guessing number HG(G) of a graph G on n vertices is defined in terms of the following game: n players are placed on the n vertices of G, each wearing a hat whose color is arbitrarily chosen from a set of q possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed.

Title: Approximation Algorithms for Stochastic Knapsack 

Abstract: The classical Knapsack problem takes as input a set of items with some fixed nonnegative values and weights. The goal is to compute a subset of items of maximum total value, subject to the constraint that the total weight of these elements is at most a given limit. In this talk we review a paper by Gupta, Krishnaswamy, Molinaro and Ravi, in which the following stochastic variation of this problem is considered: the value and weight of each item are correlated random variables with known, arbitrary distributions.

Title: Sylvester, Gallai, and their complex relatives

Abstract: Given any finite set of points in the real plane, not all collinear, there is a line in the plane that contains exactly two of them. This pretty result was conjectured by Sylvester in 1893 and proved by Gallai in 1944. We will present an extension of the result to higher dimensional complex spaces and discuss some related conjectures. This is joint work with Matthew Kroeker.

Title: Cayley graphs, association schemes and state transfer

Abstract: The aim of this talk is to give some examples of how association schemes can be used as a tool to study certain properties of Cayley graphs. In particular, they contribute to our long-term goal of characterizing perfect state transfer in Cayley graphs. The talk is based on the following paper https://arxiv.org/abs/2204.09802.

Title: Recursions and Proofs in Coxeter-Catalan combinatorics

Abstract:  The collection of parking functions under a natural Sn-action (which has Catalan-many orbits) has been a central object in Algebraic Combinatorics since the work of Haiman more than 30 years ago. One of the lines of research spawned around it was towards defining and studying analogous objects for real and complex reflection groups W; the main candidates are known as the W-non-nesting and W-non-crossing parking functions.

Title: Stochastic Minimum Norm Combinatorial Optimization

Abstract:  In this work, we introduce and study stochastic minimum-norm optimization. We have an underlying combinatorial optimization problem where the costs involved are random variables with given distributions; each feasible solution induces a random multidimensional cost vector. The goal is to find a solution that minimizes the expected norm of the induced cost vector, for a given monotone, symmetric norm. We give a framework for designing approximation algorithms for stochastic minimum-norm optimization and apply it to give approximation algorithms for stochastic minimum-norm versions of load balancing and spanning tree problems.