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Description

Partial Differential Equations seminar.

Speaker: Rishabh Gvalani.

Affiliation: Imperial College London, United Kingdom.

Date and Time: Thursday 19 September, 3:00 pm - 4:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: A mountain pass theorem in the space of probability measures and
applications.

Abstract: We prove a version of the mountain pass theorem for lower
semicontinuous and lambda-geodesically convex functionals on the space of
probability measures P(M) equipped with the W_2 Wasserstein metric,
where M is a compact Riemannian manifold or R^d. As an application of this
result, we show that the empirical process associated to a system of
weakly interacting diffusion processes exhibits a form of noise-induced
metastability. The result is based on an analysis of the associated
McKean–Vlasov free energy, which for suitable attractive interaction
potentials has at least two distinct global minima at the critical
parameter value b = b_c. Joint work with Andre Schlichting.

Rishabh Gvalani :Imperial College London, United Kingdom