Events by month

Title: Dyadic matroids with spanning cliques

*Please note time and date change

Abstract:

The Matroid Minors Project of Geelen, Gerards, and Whittle describes the structure of minor-closed classes of matroids representable over a fixed finite field.

Title: Mutually unbiased bases

Abstract:

A pair of d x d unitary matrices is unbiased if M*N is at, i.e., all its entries have the same absolute value. A relatively simple argument shows that a set of pairwise unbiased unitary matrices has size at most d + 1.

Title: Fun with Pfaffians: Identities for Schur Q-Functions

Abstract:

Schur functions determinantal identities (e.g. Jacobi-Trudi, Giambelli) are cornerstones of symmetric function theory. Less well-known are the Pfaffian identities for Schur Q-functions.

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.

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: 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: 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: 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: 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: 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: 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: 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: Graphs in algebra and algebra in graphs

Abstract:

How do algebraic properties of a graph relate to its graph theoretic properties? What are algebraic properties of graphs? What does the spectrum of a graph tell us about its structure? What is a Cayley graph?

Title: Kemeny's Constant for Markov Chains

Abstract:

Markov chains are a much-studied class of stochastic processes, and it is well-known that if the transition matrix A associated with a Markov chain possesses a certain property (called primitivity), then the long-term behaviour of the Markov chain is described by a particular eigenvector of A, known as the stationary distribution vector.

Title: Lewis Carroll and the Red Hot Potato

Abstract:

The Lewis Carroll identity expresses the determinant of a matrix in terms of subdeterminants obtained by deleting one row and column or a pair of rows and columns.

Title: New and Simple Algorithms for Stable Flow Problems

Abstract:

In the previous reading group talk we defined stable flows and saw that they always exist by a reduction to the stable allocation problem.