Departmental Colloquium
Tom Benhamou and Benjamin Call
UIC
Two RAP talks
Abstract: Singular cardinals, the forcing method and Prikry-type forcing
In the first part of this talk, we shall present an overview and give motivation for the forcing method, which is a method to produce models of set
theory. Next, we shall discuss the problems of the generalized continuum hypothesis for singular cardinals, and the problem of preserving cardinals and cofinalities.
Finally, we will introduce the main tool to work on with singular cardinals- Prikry
type forcings- which produces models where cardinals are preserved and cofinality
of some cardinals changes. More specifically, we will focus on Prikry forcing
and Magidor forcing and present recent results about those forcings.
The audience is assumed to be familiar with basic concept of set theory and
logic, such as models, ordinals and cardinals.
Unique Equilibrium States for Geodesic Flows
Equilibrium states (which are simply special invariant measures) for the geodesic flow on a compact, negatively curved manifolds, are well known to have many extremely nice properties. A natural question is what we can say when we weaken our assumptions on the geometry of our setting, for instance to nonpositively curved manifolds, or CAT(0) spaces. In this talk, we will provide a brief introduction to the theory of equilibrium states and provide an overview of recent developments in showing uniqueness and mixing properties of these measures beyond the setting of negative curvature. Finally, time permitting, we will give an idea of one of the main techniques used in recent work to handle the case of the geodesic flow on translation surfaces.
Friday September 2, 2022 at 3:00 PM in 636 SEO