Séminaire du 30 novembre 2009, 14h00: Alan
Sokal, New York University.
Some wonderful conjectures (but almost no theorems) at the
boundary between analysis, combinatorics and probability
I discuss some remarkable properties of the entire function
$F(x,y) = \sum\limits_{n=0}^\infty {x^n \over n!} \, y^{n(n-1)/2}$,
the polynomials
$P_N(x,w) = \sum\limits_{n=0}^N \binom{N}{n} x^n w^{n(N-n)}$,
and the generating polynomials
$C_n(v) = \sum\limits_{m=n-1}^{n(n-1)/2} c_{n,m} v^m$
of connected graphs.
These objects arise in several contexts in graph theory
and statistical physics.
Virginie Collette
Last modified: Mon Mar 30 14:53:58 CEST 2009