Filippo Calderoni & Daniel Lear Claveras : RAP Colloquium II/II

Posted by Ian Tobasco , part of the Departmental Colloquium.

At

Oct. 4, 2019, 3 p.m.

In

636 SEO

Abstract

This is the second of two colloquia highlighting our new Research Assistant Professors. Titles/abstracts are as follows: ------ (Filippo) Title: Recent results on permutation groups Abstract: The automorphism groups of countable homogeneous structures are natural examples of separable and completely metrizable topological groups. The richness of their topological properties have recently brought to light a crucial interplay between Fraïssé amalgamation theory and other areas of mathematics such as Ramsey theory and topological dynamics. Moreover they have been studied extensively as permutation groups. In this talk we focus on the latter aspect. We will discuss how certain model theoretic properties are used to analyze the normal subgroup structure of a large class of those groups. In particular, will see that if $M$ is the order expansion of the Fraïssé limit of a free, transitive and nontrivial amalgamation class, then $Aut(M)$ is simple. This is joint work with Kwiatkowska and Tent. ------ (Daniel) Title: Stability Near Hydrostatic Equilibrium in Fluid Mechanics Abstract: A fluid is said to be in hydrostatic equilibrium when it is at rest. Then the forces acting on it must balance it. A natural question therefore arises: What happens if our initial data is close to an hydrostatic equilibrium solution? The field of hydrodynamic stability has a long history starting in the 19th century. For us, the basic problem is to consider a perturbation of the hydrostatic equilibrium, in which case the fluid must start to move, and to study the long-time behavior of the solution.