The Allen-Cahn equation with weakly critical initial datum

Series
CDSNS Colloquium
Time
Friday, February 7, 2025 - 3:30pm for 1 hour (actually 50 minutes)
Location
Skiles 314
Speaker
Tommaso Rosati – U Warwick – T.Rosati@warwick.ac.uk – https://warwick.ac.uk/fac/sci/statistics/staff/academic-research/rosati/
Organizer
Alex Blumenthal

Please Note: Zoom link: https://gatech.zoom.us/j/91390791493?pwd=QnpaWHNEOHZTVXlZSXFkYTJ0b0Q0UT09

Motivated by question in the dynamics of phase fields, we study the Allen-Cahn equation in dimension 2 with white noise initial datum. We prove the appearance of a universal initial condition for mean curvature flow in a small noise scaling. We also obtain a weak coupling limit when the noise is not tuned down: the effective variance that appears can be described as the solution to an ODE. I will discuss ongoing applications in the perturbative study of other critical SPDEs. Joint works with Simon Gabriel, Martin Hairer, Khoa Lê and Nikos Zygouras.