Joint Event: Math Department Colloquium & SASA Seminar

• Davar Khoshnevisan
• Distinguished Professor
• University of Utah
• Date: Nov. 18, Wednesday, 2026
• Time: 14:00-14:50
• Host: Le Chen
• Room: STEM Ag 2111
• Abstract: It is a well established fact that “low-noise” parabolic systems typically reach equilibria at large times, both in the context of interacting diffusion (Carmona-Molchanov, 1999; Cox-Greven, 1994; Deuschel, 1994; Greven-den Hollander, 2007; Shiga, 1992), and in the continuous setting of stochastic partial differential equations (Assing-Manthey, 2003; Chen-Eisenberg, 2024; Chen-Ouyang-Tindel-Xia, 2026; Eckmann-Hairer, 2001; Joseph-Khoshnevisan-Kim-Mueller, 2026+; Misiats-Stanzhytskyi, 2020; Gu-Li, 2020; Tessitore-Zabczyk, 1998). The principal aim of this talk is to present results in the quite different “very high noise” regime — this includes many typical systems in 1+1 and 1+2 dimensions — where we show that the system is dissipative; somewhat more precisely, that a very large part of the system (the so-called “valleys”) uniformly tends to zero as time tends to infinity. Such results were known until recently only in 1+1 dimension (Khoshnevisan-Kim-Mueller-Shiu, 2020; Khoshnevisan-Kim-Mueller, 2024) and when the external forcing was space-time white noise. The main new ideas involve the identification of the maximal solution to certain non-linear differential inequalities, as well as coarse-graining ideas of Berger, Caravenna, and Turchi (2025+). This is based on joint work with Kunwoo Kim (POSTECH), Carl Mueller (Rochester), and Mathew Joseph (ISI-Bangalore).