Future students

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.

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: 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: 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.