Current students

Title: Reverse plane partitions via quiver representations

Abstract:

Let $\lambda$ be a partition. The reverse plane partitions of shape $\lambda$ are a kind of filling of the Ferrers diagram of $\lambda$ by non-negative integers. Richard Stanley found the generating function which enumerates them according to the sum of the entries.

Title: Stable Flows

Abstract:

We describe a flow model that generalizes ordinary network flows the same way as stable matchings generalize the bipartite matching problem.

Title: Incidence bialgebras of monoidal categories

Abstract:

We begin with Joni and Rota's definition of the incidence coalgebra of a category or partially ordered set and then discuss some cases where a monoidal product on a category turns this coalgebra into a bialgebra.

Title: From Combinatorics to Computer Algebra and Morse Theory - Making Sense of Multivariate Asymptotics

Abstract:

The  asymptotic study  of  multivariate  generating  functions comprises  the  domain  of  Analytic Combinatorics  in Several Variables (ACSV).

Title: QAOA Versus Classical

Abstract: 

There has been a back and forth about whether the QAOA algorithm of Farhi, Goldstone and Gutmann can in some sense be duplicated classically.

Title: On the approximability of the stable matching problem with ties of size two and one-sided ties

Abstract:

The stable matching problem is central for game theory. If participants are allowed to have ties, the problem of finding a stable matching of maximum cardinality is an NP-hard problem, even when the ties are of size two.

Title: Indicence groups of graphs, forbidden minors, and planar covers

Abstract:

The solution group of binary linear system is a quantum-probabilistic generalization of the solution space of the system.

Title: A (1 + 1/e)-Approximation Algorithm for Maximum Stable Matching with One-Sided Ties and Incomplete Lists

Abstract:

We will continue the discussion of stable matching when there are unacceptable pairs and one-sided ties. Two weeks ago, we looked at a 3/2-approximation that was purely combinatorial. 

Title: Feynman graphs to chord diagrams

Abstract:

I will explain how classic techniques of algebraic combinatorics can, via chord diagrams, tell us about the leading log, next-to-leading log, etc, expansions in quantum field theory, and what we think chord diagrams can tell us about individual Feynman graphs as well. 

Title: Quasi-popular Matchings, Optimality, and Extended Formulations

Abstract:

The goal of this talk is to obtain efficient algorithms for computing desirable matchings (wrt cost) by paying the price of mildly relaxing popularity.