The KPZ equation is a stochastic PDE which was introduced in 1986 by Khardar, Parisi, and Zhang as a model for surface growth. A remarkable connection between the KPZ equation and the Airy point process was found in 2011 by Amir, Corwin and Quastel and reformulated in 2016 by Borodin and Gorin. I will show how this connection can be used to characterize the KPZ solution in terms of a 2x2 Riemann-Hilbert problem, and how this Riemann-Hilbert characterization can be used to derive uniform lower tail asymptotics of the KPZ equation.
This is based on joint work in progress with Mattia Cafasso (Angers).
Alexi Morin Duchesne
