# Some wonderful conjectures (but almost no theorems) at the boundary between analysis, combinatorics and probability

#### by Alan Sokal

Institution: University College London/New York University
Date: Thu 29th July 2010
Time: 10:00 AM
Location: Old Geology Theatre 1, The University of Melbourne

Abstract: I discuss some analytic and combinatorial properties of the entire function
$F(x,y) = \sum\limits_{n=0}^\infty \frac{x^n}{n!} y^{n(n-1)/2}$.
This function (or formal power series) arises in numerous problems in enumerative combinatorics, notably in the enumeration of connected graphs.