## Upcoming Seminars

Math Seminar: Mixing and the Glass Transition
Aaron Smith,  University of Ottawa, Department of Mathematics and Statistics
February 1, 2019
11:20-12:20
Armitage Hall Room 121

• Supercooled liquid forms when a liquid is cooled below its usual freezing temperature without entering a crystalline solid phase. As supercooled liquids continue to get colder, they exhibit something called the glass transition: they remain disordered, but start to otherwise behave much like solids. This glass transition is important for many materials, including rubbers and colloids, but is not theoretically well-understood. In this talk I will introduce a simple model for the glass transition that is easy to understand but difficult to study. I will then introduce two related families of models, introduced by physicists, that seem to give similar “glassy” behavior. Finally, I will present some heuristics and recent results on the relaxation and mixing behavior of these two models. My results in this talk are from joint and ongoing work with Paul Chleboun, Alessandra Faggionato, Fabio Martinelli, Natesh Pillai and Cristina Toninelli.

Math Seminar: Non-local Navier-Stokes equations
Camillo De Lellis,  Institute of Advanced Study in Princeton, NJ
February 22, 2019
11:20-12:20
Armitage Hall Room 121

• I will consider a variant of the Navier-Stokes equations, where the classical Laplacian is substituted by a fractional Laplacian $-(-\Delta)^\alpha$. I will present two results. In the hypodissipative case, i.e. when $\alpha$ is sufficiently small, in a joint work with Maria Colombo and Luigi De Rosa we show that Leray solutions are ill-posed. In the hyperdissipative case, i.e. when $\alpha>1$, in a joint work with Maria Colombo and Annalisa Massaccesi we prove a “strong analog” of the Caffarelli-Kohn-Nirenberg Theorem, which strengthens the conclusions of a previous work by Katz and Pavlovic.

See next page.