Abstract: Discrete harmonic and discrete holomorphic functions have been proved to be very useful in many domains of mathematics. Recently, they have been at the heart of the two dimensional statistical physics (for instance, through the works of Kenyon, Schramm, Smirnov and others...). We will present some of the connections between discrete complex analysis and statistical physics. In particular (it is a joint work with S. Smirnov), we will use discrete holomorphic functions to prove that the number a_n of self-avoiding walks of length n (starting at the origin) on the hexagonal lattice satisfies:

a_n^{1/n} ----> sqrt(2 + sqrt(2))

when n tends to infinity. This confirms a conjecture made by Nienhuis in 1982.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006