Events

Title: Electrical networks, random spanning trees, and matroids

Abstract:

This is a reprise of a survey talk I gave at the East Coast Combinatorics Conference in August 2019, and a variation of one I gave in the graphs and matroids seminar last year.

Title: The Capacitated Survivable Network Design Problem

Abstract:

The Capacitated Survivable Network Design Problem or Cap-SNDP models a network reinforcement problem where the network designer wants to find a minimum-cost set of reinforcements that protects the network from an adversary.

Title: Some places matroids appear in quantum field theory and some places I would like them to

Abstract:

I will discuss some places matroids have appeared in my work in quantum field theory, including some older work on numerator structure with Dirk Kreimer and some work in progress with Iain Crump on period identities.

Title: Uniformly generate graphs with given degrees rapidly

Abstract:

I will survey the research on exact/approximate uniform generation of graphs with prescribed degrees.

Title: On the Strong Nine Dragon Tree Conjecture

Abstract:

Nash-Williams forest covering theorem says that a graph decomposes into $k$ forests if and only if it has fractional arboricity at most $k$. In 2012 Mickeal Montassier, Patrice Ossona de Mendez, Andre Raspaud, and Xuding Zhu  proposed a significant strengthening of Nash-Williams Theorem, called the Strong Nine Dragon Tree Conjecture.

Title: Random Pattern-Avoiding Permutations

Abstract:

A "pattern of length k" is simply a permutation of {1,..,k}.  This pattern is said to be contained in a permutation of {1,...,N} (for N>k) if there is a subsequence of k elements of the (long) permutation that appears in the same relative order as the pattern.

Title: Excluding a ladder

Abstract:

A folklore result says that if a graph does not contain the path of length k as a subgraph, then it has tree-depth at most k.

Title: Network Design $s$-$t$ Effective Resistance

Abstract:

We consider a problem of designing a network with small $s$-$t$ effective resistance. In the problem, we are given an undirected graph $G=(V,E)$, two designated vertices $s,t \in V$, and a budget $k$.

Title: Minimum degree conditions for Hamilton cycles in hypergrahs

Abstract:

A classic result of Dirac states that a graph in which every vertex is connected to at least half of the other vertices contains a Hamilton cycle. How can we generalize Dirac's theorem to hypergraphs?

Title: Moore Graphs

Abstract:

Moore graphs were introduced by Hoffman and Singleton in a fundamental paper. They can be defined as graphs with diameter $d$ and girth $2d+1$.