Francqui chair 2010-2011: Prof. Alain Valette

Professor Alain Valette holds the Francqui Chair 2010-2011 at the Department of Mathematics, K.U.Leuven. Alain Valette is a professor of mathematics at the Université de Neuchâtel (Switzerland) and has published numerous books and articles in group theory, functional analysis and geometry.

Inaugural lecture Graphs with large girth

Date: Wednesday, February 16, 2011, at 18h00. The inaugural lecture will be followed by a reception.

Location: KULAK, Auditorium A305, building A, Etienne Sabbelaan 53, Kortrijk. How to get there?

Registration: The registration is now closed.

Abstract:
The girth of a graph is the length of the shortest circuit. When a graph is viewed as a communication network, it is often desirable to ask for the largest possible girth, to avoid redundancies. It is easy to see that the girth of a finite regular graph is at most logarithmic in the number of vertices. In 1963, it was proved by Erdös and Sachs, in a non-constructive way, that there exists infinite families of regular graphs (of fixed degree) whose girth is actually logarithmic in the number of vertices. Explicit families were constructed in 1986, independently by Margulis and Lubotzky-Phillips-Sarnak: for every prime p congruent to 1 modulo 4, and every odd prime q, there exists p+1 generators of the group PSL(2,q) such that the corresponding Cayley graph has logarithmic girth in q. We will give a reasonably elementary proof of this fact, based on Jacobi's 4-square theorem, the arithmetic of integer quaternions, and the structure of the group PSL(2,q). That proof is joined work with G. Davidoff and P. Sarnak.

Francqui lecture series Metric embeddings in Hilbert and Banach spaces

Abstract:
In the last years, there was a remarkable convergence between three seemingly remote fields of mathematics: theoretical computer science, geometry of Banach spaces, K-theory of C*-algebras. The common theme is embeddings of discrete metric spaces into Hilbert or Banach spaces. Learning of techniques from other fields allowed for mutual cross-fertilization, and it is the purpose of this set of lectures to present some recent developments in this fascinating subject.

Lecture notes:

• Notes of the first 4 lectures (February 28 and March 1).
• Notes of lectures 5 and 6 (March 7).
• Notes of lectures 7 and 8 (March 8).
• List of references.

Francqui Foundation

The Francqui Chair is financed by the Francqui Foundation.