# Caltech/UCLA Joint Analysis Seminar

*,*Assistant Professor

*,*Mathematics Engineering

*,*University of Chile

*,*

The height function associated to the asymmetric simple exclusion process (ASEP) is one of the

canonical models of random interface growth belonging to the KPZ universality class. As such, there are very

precise conjectures about the size and distribution of its fluctuations, which are related in many cases to random matrix theory.

In this talk I will describe recent progress in the study of the ASEP height function starting from half-flat and flat initial data.

I will present explicit formulas for certain generating functions of the model, which in the flat case can be expressed as a Fredholm

Pfaffian. I will also explain how these formulas can be used to provide formal derivations of the conjectured limiting fluctuations,

and discuss partial progress towards rigorous proofs of these limits as well as related results for the KPZ equation. Based on joint work

with Janosch Ortmann and Jeremy Quastel.