Departmental Colloquium
Filippo Calderoni & Daniel Lear Claveras
UIC
RAP Colloquium II/II
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.
Friday October 4, 2019 at 3:00 PM in 636 SEO