Mathematical Sciences Research Institute

Home » Definability, decidability, and computability in number theory, part 2


Definability, Decidability, and Computability in Number Theory, part 2 July 18, 2022 to August 12, 2022
Organizers Valentina Harizanov (George Washington University), Barry Mazur (Harvard University), Russell Miller (Queens College, CUNY; CUNY, Graduate Center), Jonathan Pila (University of Oxford), Thomas Scanlon (University of California, Berkeley), Alexandra Shlapentokh (East Carolina University)
Image edited
Title page of Diophantus' Arithmetica - ETH Zurich
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.
Keywords and Mathematics Subject Classification (MSC)
  • number theory

  • model theory

  • computability theory

  • first-order and Diophantine definability

  • Hilbert's Tenth Problem

  • Diophantine equations

  • Diophantine stability

  • Diophantine geometry

  • ranks of abelian varieties

  • field arithmetic

  • function fields

  • number fields

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Logistics Program Logistics can be viewed by Members. If you are a program member then Login Here.
Programmatic Workshops Workshop dates have not yet been selected