Title: Complex dynamics of excitable McKean-Vlasov dynamics and applications to Parkinson’s disease

Abstract: In this talk, I will present a few properties of McKean-Vlasov equations representing the dynamics of large networks of neurons. Neurons are typically described as excitable systems: each has a globally stable state corresponding to rest, but perturbations exceeding a threshold lead to transient large excursions away from the resting state. I will present here a combination of...

Title: Sobolev embedding from and to geometric viewpoints

Abstract: We will present the geometric properties of functions in Sobolev space and a proof of the embedding theorem using isoperimetric inequality using rearrangements.

Speaker: Buddhika Nettasinghe, Dept. of Business Analytics

Speaker: Mehrdad Moharrani, Department of Computer Science

Title: Conditional Positive Definiteness and Complete Monotonicity in Subnormal Operator Theory