Events

Title: Counting matroid extensions

Abstract: In this talk, we will discuss methods of counting the number of extensions of certain matroids. We will see that, in some cases, the number of extensions is surprisingly large. I will start by introducing matroids, so previous experience with matroids is not assumed.

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: To be annouced.

Abstract: To be announced.

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: Budget Feasible Mechanisms : Part II

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: 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: Bipartite determinantal ideals and concurrent vertex maps

Abstract: The classical determinantal ideals play an important role in commutative algebra, algebraic geometry, representation theory and combinatorics. They can be generalized to bipartite determinantal ideals which are the defining ideals of Nakajima's affine graded quiver variety. In this talk, we will introduce a combinatorial model called concurrent vertex maps to describe the Stanley-Reisner complex of the initial ideal of any bipartite determinantal ideal, and study properties and applications of this model.

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: Geometric approach to some rank 3 graphs

Abstract: Rank 3 graphs are graphs whose full automorphism group acts as a rank 3 group on the vertices. Finite rank 3 groups are classified and hence finite rank 3 graphs are classified. The main examples arise from geometric structures such as projective and polar spaces, and there is one class of examples related to the exceptional groups of type E6. We present a combinatorial/geometric/projective construction of these graphs.  We then consider a class of regular sets, that is, subsets S of the vertices such that the number of vertices of S adjacent to some vertex v only depends on whether v belongs to S or not. We will explain how this leads to characterizations of certain automorphisms of the E6 graphs and other graphs.

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.