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Decidability, definability and computability in number theory: Part 1 - Virtual Semester August 17, 2020 to December 18, 2020
Organizers LEAD Valentina Harizanov (George Washington University), Maryanthe Malliaris (University of Chicago), Barry Mazur (Harvard University), Russell Miller (Queens College, CUNY; CUNY, Graduate Center), Jonathan Pila (University of Oxford), Thomas Scanlon (University of California, Berkeley), LEAD Alexandra Shlapentokh (East Carolina University), Carlos Videla (Mount Royal University)
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Title page of Diophantus' Arithmetica - ETH Zurich
Until further notice, the MSRI building will only be open to a small group of essential staff and members of the Fall 2020 scientific programs. All scientific activities will be available online so that those who can't attend in person are able to participate. If you are not a member of the program and would like to participate in any of the online activities, please fill out this REGISTRATION FORM. ONLINE SEMINARS Five Minute Talks   Five Minute Talks Schedule September 1st and 3rd Diophantine Problems Mondays at 9:00am Pacific Time Organizers: Hector Pasten and Natalia Garcia-Fritz DDC Junior Seminar Tuesdays at 9:00am Pacific Time Organizers: Russell Miller and Lynn Scow Valuation Theory Wednesdays at 9:00am Pacific Time Organizers:Franziska Jahnke, Sylvy Anscombe, and Philip Dittmann Definability Seminar Wednesdays at 10:00am Pacific Time Organizers: Kirsten Eisentraeger and Jennifer Park Note: will not meet every Wednesday Reading Group: valuations on dp-finite fields Thursdays at 8:00am Pacific Time Organizer: Franziska Jahnke  DDC Seminar (main weekly seminar) Alternating Thursdays and Fridays at 9:00am Pacific Time Organizers: Sasha Shlapentokh, Valentina Harizanov Computability Theory Alternating Thursdays and Fridays at 9:00am Pacific Time Organizer: Valentina Harizanov PROGRAM DESCRIPTION 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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