RTG Colloquium - Winter Term 2025/2026

Weak KPZ universality of the stochastic heat equation

Prof. Dr. Alejandro Ramirez (NYU Shanghai)

The KPZ universality describes fluctuations of a one dimensional interface separating a stable phase from an unstable one. This kind of behavior has been proven only for a few mathematical models, most of them  "directed", meaning that paths visit points at most once. Weak KPZ universality, refers to a rescaling towards the 1+1 stochastic heat equation, for which KPZ universality is expected. We describe one of the few instances where weak KPZ universality has been established for a non-directed model:  the planar stochastic heat equation with spatial white noise, corresponding to a Skorokhod interpretation of  integrals.  This talk is based on a joint work with Jeremy Quastel and Balint Virag.

Detailed programme of the event:

4 p.m. (sharp) in SRZ 216/217: introductory talk for PhD students and postdocs by Bastián Mora García
4.30 p.m.: coffee and tea will be served in the Cluster Lounge (Orléans-Ring 12)
5 p.m. (sharp) in SRZ 216/217: Colloquium-talk by Prof. Dr. Alejandro Ramirez
 

Effective ellipticity for high contrast homogenization

Prof. Dr. Antoine Gloria (Sorbonne Université & Université Libre de Bruxelles)

Abstract: Homogenization is the art of averaging coefficients of differential operators in a consistent way. It is the mathematical theory associated with composite materials. The theory is by-now well-understood for linear elliptic equations with random coefficients that are uniformly bounded and elliptic. For applications to mathematical physics and to more contemporary homogenization problems, it is however desirable to move away from uniform ellipticity. In this colloquium I will introduce a concept of effective ellipticity field and ellipticity radius, which quantifies how and at which scale an elliptic operator with (degenerate and unbounded) stationary ergodic coefficients is close to a uniformly elliptic operator. Combined with nonlinear concentration of measure, this allows to extend quantitative homogenization theory to the setting of high- (and even infinite-) contrast.

Detailed programme of the event:   

• 4 p.m. (sharp) in SRZ 216/217: introductory talk for PhD students and postdocs by Dr. Francesco Deangelis 
• 4.30 p.m. coffee and tea will be served in the Cluster Lounge (Orléans-Ring 12)
• 5 p.m. (sharp) in SRZ 216/217: Colloquium-talk by Prof. Dr. Antoine Gloria 
• 6 p.m. informal reception in the Cluster Lounge (Orléans-Ring 12)