## Decidability, Definability and Computability in Number Theory

**Date:**
17 August - 18 December 2020

**Location: ** Online from MSRI

**Event type:**
Extended Format

**Organisers: ** Valentina Harizanov (GWU), Maryanthe Malliaris (Chicgo), Barry Mazur (Harvard), Russell Miller (CUNY), Jonathan Pila (Oxford), Thomas Scanlon (Berkeley), Alexandra Shlapentokh (East Carolina), Carlos Videla (Mount Royal)

**Website:**www.msri.org/programs/319

This program is focused on the two-way interaction of logical ideas and techniques, such as definability from model theory and decidability from computability theory, with fundamental problems in number theory. These include analogues of Hilbert’s tenth problem, isolating properties of fields of algebraic numbers which relate to undecidability, decision problems around linear recurrence and algebraic differential equations, the relation of transcendence results and conjectures to decidability and decision problems, and some problems in anabelian geometry and field arithmetic. We are interested in this specific interface across a range of problems and so intend to build a semester which is both more topically focused and more mathematically broad than a typical MSRI program.

Professor François Loeser (Sorbonne) has been appointed as a Clay Senior Scholar to participate in this program.

CMI Enhancement and Partnership Program