Mathematical Sciences Research Institute

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Decidability, definability and computability in number theory August 17, 2020 to December 18, 2020
Organizers Valentina Harizanov (George Washington University), Moshe Jarden (Tel-Aviv University), Maryanthe Malliaris (University of Chicago), Barry Mazur (Harvard University), Russell Miller (Queens College, CUNY), Jonathan Pila (University of Oxford), LEAD Thomas Scanlon (University of California, Berkeley), Alexandra Shlapentokh (East Carolina University), Carlos Videla (Mount Royal University)
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
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