Mark Pullins (CU) Generically 2-transitive actions of linear algebraic groups with solvable point stabilizers

Tue, Feb. 25 2pm (MATH 220)

Logic

Michael Wheeler (CU Boulder)

X

We will explore the structure of SOP_2 types (defined by Malliaris and Shelah) and types whose realizations fill cuts in regular ultrapowers of infinite linear orders. We will see that both sorts of types and their distributions can be characterized by certain classes of graphs. This will extend to a new characterization of good ultrafilters. Part 1 will motivate the study of these types in terms of Keisler's order on countable complete first-order theories.

Graph-like Types and Good Ultrafilters, Part 1

Tue, Feb. 25 4pm (Math 350)

Noncomm Geometry

Florian Naef (MIT)

X

Given a manifold M, Chas and Sullivan construct a Lie bialgebra structure on the homology of the space of (unparametrized) loops using intresections and self-intersections of loops. We give an algebraic description of this structure under Chen's isomorphism identifying loop space homology with cyclic homology. More precisely, we construct a homotopy involutive Lie bialgebra structure on cyclic cochains that depends on the partition function of a Chern-Simons type field theory. Moreover, we discuss the (non-)homotopy invariance of that structure and its relation to the configuration space of two points.

String topology and the configuration space of two points

Tue, Feb. 25 4pm (MATH 350)

Topology

Florian Naef (MIT)

X

Given a manifold M, Chas and Sullivan construct a Lie bialgebra structure on the homology of the space of (unparametrized) loops using intresections and self-intersections of loops. We give an algebraic description of this structure under Chen's isomorphism identifying loop space homology with cyclic homology. More precisely, we construct a homotopy involutive Lie bialgebra structure on cyclic cochains that depends on the partition function of a Chern-Simons type field theory. Moreover, we discuss the (non-)homotopy invariance of that structure and its relation to the configuration space of two points.

String topology and the configuration space of two points