Alexander Belton (Lancaster University)

An introduction to Hirschman-Widder densities and their preservers

Hirschman-Widder densities may be viewed as the probability density functions of positive linear combinations of independent and identically distributed exponential random variables. They also arise naturally in the study of Pólya frequency functions, which are integrable functions that give rise to totally positive Toeplitz kernels. This talk will introduce the class of Hirschman-Widder densities and discuss some of its properties. We will demonstrate connections to Schur polynomials and to orbital integrals. We will conclude by describing the rigidity of this class under composition with polynomial functions.

This is joint work with Dominique Guillot (University of Delaware), Apoorva Khare (Indian Institute of Science, Bangalore) and Mihai Putinar (University of California at Santa Barbara and Newcastle University).

Bishal Deb (University College London)

Multivariate continued fractions associated to Genocchi and median Genocchi numbers

In a seminal paper in 1980, Flajolet laid out the combinatorial theory of continued fractions where he gave combinatorial interpretations for Stieltjes and Jacobi type continued fractions in terms of Dyck and Motzkin paths, respectively. In this talk, we shall look at continued fractions for multivariate generalisations for the Genocchi and median Genocchi that count several statistics for a class of permutations called D-permutations. This is based on ongoing joint work with Alan Sokal.

Tony Guttmann (University of Melbourne)

Asymptotics, Steiltjes moment sequences and Polya frequency sequences

In this rambling talk I will discuss the extraction of asymptotics from a finite number of terms of the generating function of combinatorial sequences, and the benefits/significance of knowing that these are Stieltjes moment sequences or Polya frequency sequences. Particular application to pattern-avoiding permutation sequences will be made.

Slim Kammoun (University of Bristol)

On the longest common subsequence of i.i.d permutations

Greta Panova (University of Southern California)

The world of poset inequalities

‌Jiang Zeng (University of Lyon)

Equidistribution of permutation statistics and continued fractions

We will survey some recent results and problems about the equidistribution of permutation statistics. Most of the results are proved using the combinatorial theory of Jacobi-type continued fractions or bijections.