## Noncommutative Geometry Seminar

**Date:** November 13, 2019

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 220

**Speaker:** Paul Schupp, University of Illinois at Urbana Champaign

**Title:** *Closures of Turing Degrees*

**Abstract:** This talk is on aspect of my general project with Carl Jockusch on “the coarsification of computability theory”, that is, bringing the asymptotic-generic point of view of geometric group theory into the theory of computability. Classically, computability theory studies Turing degrees, that is, equivalence classes of subsets of N which are computationally equivalent. Coarse computability studies how closely arbitrary subsets of N can be approximated by computable sets. The idea of coarse computabilty leads to a natural definition of the closure of a Turing degree in the space S of coarse similarity classes of subsets of N with the Besicovich metric. It turns out that S is an interesting space. We will discuss interactions of the topology of S and properties of Turing degrees.