Dear colleagues, we are happy to announce the following online talk: Speaker: Vincent Martinez (CUNY Hunter College) Title: On unique ergodicity, regularity, and mixing for the weakly-damped stochastic KdV equation. Abstract: We discuss the existence, uniqueness, and regularity of invariant measures for the damped-driven stochastic Korteweg-de Vries equation, where the noise is additive and sufficiently non-degenerate. It is shown that a simple, but versatile control strategy, typically employed to establish exponential mixing for strongly dissipative systems such as the 2D Navier-Stokes equations, can nevertheless be applied in this weakly dissipative setting to establish elementary proofs of both unique ergodicity, albeit without mixing rates, as well as regularity of the support of the invariant measure. Under the assumption of large damping, however, a one-force, one-solution principle is established, from which we are able to deduce the existence of a spectral gap with respect to a Wasserstein distance-like function. Date and time: Monday June 14, 17:30-18:30 (Rome time zone) Zoom link: https://us02web.zoom.us/j/85740643260?pwd=SzFjTXo0bWE3YjI3VWo0b3krT09kdz09 ID riunione: 857 4064 3260 Passcode: w7yJLi This talk is the fourth of the (PMS)^2: Pavia-Milano Seminar series on Probability and Mathematical Statistics organized jointly by the universities Milano-Bicocca, Pavia, Milano-Politecnico and Milano-Statale. Participation is free and welcome! (though limited to 100 participants for technical reasons). Best regards The organizers (Mario Maurelli, Carlo Orrieri, Maurizia Rossi, Margherita Zanella)