Events - July 2023

Title: Hardness of pricing routes for two-stage stochastic vehicle routing problems with scenarios, Part II

Abstract: Following state-of-the-art exact algorithms for vehicle routing problems, several recent exact algorithms for the two-stage vehicle routing problem with stochastic demands (VRPSD) are based on set partitioning formulations. To solve the corresponding LP relaxation, these algorithms rely on efficient routines for solving the associated pricing problems. In this paper, we study the complexity of solving such VRPSD pricing problems.

Title: Cluster chromatic number of $G(n,p)$

Abstract: A colouring of a graph $G$ is said to be $\kappa$-clustered if no colour class has a connected component with more than $\kappa$ vertices. In this talk, we give the $\kappa$-clustered chromatic number of $G(n,p)$ for $\kappa$ increasing at various rates with respect to $n$.

The talk is joint work with Jane Gao.

Title: Hardness of pricing routes for two-stage stochastic vehicle routing problems with scenarios

Abstract: Following state-of-the-art exact algorithms for vehicle routing problems, several recent exact algorithms for the two-stage vehicle routing problem with stochastic demands (VRPSD) are based on set partitioning formulations. To solve the corresponding LP relaxation, these algorithms rely on efficient routines for solving the associated pricing problems. In this paper, we study the complexity of solving such VRPSD pricing problems.

Title: Combinatorial and complexity theoretic aspects of Stabilities and Controllabilities of linear switched systems(discrete and continuous time)

Abstract: I will talk about my "pre-hyperbolic" research, some of it done jointly with Alex Samorodnitsky and Alex Olshevsky.

Title: Budget Feasible Mechanisms

Abstract: In the setting of budget feasible mechanism design, a buyer wants to purchase items from a set of agents. Each agent can supply at item at an incurred cost of c_i to themself, and the buyer wants to optimize over their own valuation for the set of items bought. The cost c_i is private information that the buyer doesn't have access to. The goal is to design a mechanism that is truthful, in the sense that the sellers do not have incentive to deviate from reporting their true costs, and budget feasible, in the sense that the total payments made to the sellers is within some budget B.

Title: On the eigenvalues of the graphs D(5,q)

Abstract: In 1995, Lazebnik and Ustimenko introduced the family of q-regular graphs D(k, q), which is defined for any positive integer k and prime power q. The connected components of the graph D(k, q) have provided the best-known general lower bound on the size of a graph for any given order and girth to this day.

Title: Thin distance-regular graphs with classical parameters $(D,q,q,\frac{q^{t}-1}{q-1}-1)$ with $t> D$ are the Grassmann graphs

Abstract: In the survey paper by Van Dam, Koolen and Tanaka (Distance-regular graphs, Electron. J. Comb., Dynamic Survey (2016), \#DS22), they asked to classify the thin $Q$-polynomial distance-regular graphs. In this talk, we will discuss our result which states that the Grassmann graphs with large diameter are characterized by their intersection numbers under the extra condition that they are thin.

This is joint work with Jack Koolen and Ying-Ying Tan.

Title: Budget Feasible Mechanisms

Abstract: In the setting of budget feasible mechanism design, a buyer wants to purchase items from a set of agents. Each agent can supply at item at an incurred cost of c_i to themself, and the buyer wants to optimize over their own valuation for the set of items bought. The cost c_i is private information that the buyer doesn't have access to. The goal is to design a mechanism that is truthful, in the sense that the sellers do not have incentive to deviate from reporting their true costs, and budget feasible, in the sense that the total payments made to the sellers is within some budget B.

Title: Modular representations of the symmetric group and categorification (part I)

Abstract: I'll give two talks on the representations of the symmetric group over small finite fields, in particular, their block structure, with an emphasis on the perspective from categorical actions of Lie algebras.  No previous background in modular representation theory will be assumed.