Abstract：

I will review joint work with F. Caravenna and N. Zygouras on the directed polymer model, the stochastic heat equation (SHE), and the KPZ equation in the critical dimension 2, which eventually led to our construction of the Critical 2D Stochastic Heat Flow (SHF). The SHF provides a candidate solution to the 2D SHE, a critical singular SPDE that lies beyond the scope of existing solution theories, and it gives a rare example of a non-Gaussian scaling limit for a model at its phase transition point in the critical dimension.

About the speaker：

Rongfeng Sun is a professor in the Department of Mathematics at the National University of Singapore (NUS). He received his PhD in 2004 from the Courant Institute of Mathematical Sciences at New York University. He then did postdoctoral research at EURANDOM, TU Eindhoven from 2004-2006 and at TU Berlin from 2006-2008, before joining NUS in 2008. His research interests lie in interacting particle systems, disordered systems, and their scaling limits. He has served on the editorial boards of Mathematical Physics, Analysis and Geometry, Electronic Communications in Probability/Electronic Journal of Probability, and Annals of Applied Probability. He delivered the Lévy Lecture in SPA 2024 and is an invited speaker in the ICM 2026.