Seminar

Title: Maximum Cardinality Popular Matchings

Abstract:

We have seen the algorithm by Abraham, Irving, Kavitha, and Mehlhorn which deals with finding popular matchings (can be easily modified to give maximum cardinality popular matchings) in bipartite graphs with one-sided preference lists.

Title: The Parallel Postulate: a 2000-year controversy

Abstract:

Euclid's book The Elements was groundbreaking in its logical formulation of synthetic geometry, and it is profoundly influential to this day, as it is widely considered to be the most published non-religious book in human history.

Title: Finding perfect matchings in random regular graphs in linear expected time

Abstract:

In a seminal paper on finding large matchings in sparse random graphs, Karp and Sipser proposed two algorithms for this task. The second algorithm has been intensely studied, but due to technical difficulties, the first algorithm has received less attention. Empirical results suggest that the first algorithm is superior.

Title: Arborified zeta values and shuffles of rooted trees

_{*Please note room change}

Abstract:

Arborified zeta values are a generalisation to rooted trees of the usual multizeta values.

Title: Matching Games: From Bargaining to the Nucleolus

Abstract:

Cooperative matching games were first introduced in seminal work by Shapley and Shubik in their classic 1971 paper. In this talk, I will first review some of the key concepts and results in this area. I will then use these tools to (re-)derive several facts and algorithms for network generalizations of the famous Nash bargaining concept.

Title: Spanning trees and electrical networks... and what about matroids?

Abstract:

The relevance of spanning trees to the theory of electrifcal networks goes all the way back to Kirchhoff in 1847.

Title: Popularity, Mixed Matchings, and Self-duality

Abstract:

This week we continue our discussion of popular matchings.

Title: Popular Matchings

Abstract:

We introduce a variant of the stable matching problem on a bipartite graph G = (A [ P;E)

Title: Approximately counting independent sets in graphs with bounded bipartite pathwidth

Abstract:

In 1989, Jerrum and Sinclair showed that a natural Markov chain for counting
matchings in a given graph G is rapidly mixing.

Title: Hedetnemi's conjecture is false

Abstract:

On may 6th 2019, Yaroslav Shitov found a graph G x H such that the chromatic number of G x H is strictly smaller than the minimum of the chromatic number of G and the chromatic number of H. I will present the example.