## 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.