We discuss invariant, definable, and finitely satisfiable types in theories with NIP.
Gromov defined a class of groups called hyperbolic groups and associated a boundary space to each. A natural question arises: if H¡G are hyperbolic groups, does inclusion induce a map from the boundary of H to that of G? Such a map, when well-defined, is called a Cannon-Thurston map after a family of examples constructed by Cannon and Thurston.
This is the first session of a new learning seminar in geometry and topology. The plan is to work through Milnor's Morse Theory. This first talk will be covering some background in topology to set us up to start attacking the book. Join us!
Alexandr Kazda showed in 2010 that Maltsev digraphs have a majority polymorphism. Coincidently, the paper in which the proof appeared has the same title as this talk. I will present the proof.
We derive a projection analog of the usual continuous functional calculus and show how it can be used to simplify and strengthen a number of classical results about projections in C*-algebras, particularly those of real rank zero.
In this I will first introduce the growth rate of a Coxeter group. This is a number associated to such a group, which turns later on to be a nice algebraic integer (Salem or Pisot number) if the group acts on the hyperbolic space of dimension n = 2 or 3.
We investigate non-degenerate Lagrangians of the form
f(ux,uy,ut)dxdydt
We present products and Morley sequences of invariant types, and give an application to denable groups.
Gromov’s theorem states that a finitely generated group of polynomially bounded growth has a nilpotent subgroup of finite index. I hope to give a complete proof of Gromov’s theorem over a few lectures. The first lecture is intended to be accessible to a beginning graduate student and will give the basic background needed along with an overview of the main steps of the proof.
We will continue covering the background required to get stuck in to Milnor’s Morse Theory. We will finish talking about CW-complexes and then cover smooth manifolds, tangent spaces and smooth functions between manifolds. With a bit of luck we will get through some of the basic definitions of Morse Theory. Come along if you dare!