Events

On the chromatic number of random d-regular graphs

Abstract:

Achlioptas and Moore have announced a proof that random d-regular graphs asymptotically almost surely (a.a.s.) have chromatic number k-1, k, or k+1 where k is the smallest integer satisfying d < 2(k-1)\log(k-1).

Packing Element-Disjoint Steiner Trees

Abstract:

We present some hardness results and approximation algorithms for the problem of packing element-disjoint Steiner trees in graphs.

Constructing expander graphs from the Generalized Riemann Hypothesis

Abstract:

We present a construction of expander graphs obtained from Cayley graphs of narrow ray class groups, whose eigenvalue bounds follow from the Generalized Riemann Hypothesis.

Continuity of quantum channel capacities

Abstract:

Jeu de Taquin and Wronskians of polynomials

Abstract:

Jeu de taquin was first introduced by Schutzenberger in the 1970s, and is now considered a fundamental construction in the combinatorics of Young tableaux.

Fermat quotients

Abstract:

We describe recent results improving previous estimates of H. W. Lenstra and A. Granville on the smallest non-zero Fermat quotient. This question is motivated by application to square-free testing (H. W. Lenstra), Fermat Last Theorem (A.

Recent results on planarity

Abstract:

Three well-known characterizations of planarity of graphs are the theorems of Kuratowski, MacLane, and Whitney. The first is about forbidden subgraphs, the second about a basis for the cycle space, and the third is about dual graphs.

The Asymptotic Enumeration of Maps

Abstract:

One area founded by W. T. Tutte in the 1960s is the enumeration of planar maps, graphs drawn in the plane with n edges.

Inequivalent representations of matroids

Abstract:

In joint work with Bert Gerards and Geoff Whittle, we showed that 4-connected matroids have a bounded number of inequivalent representations over fields of prime order. At the time we were confident that we could extend this to all finite fields.

Portfolio Optimization

Abstract:

This talk will begin with an overview of the subject (for those who may not be too familiar with it). Then I will discuss several areas of my research.