Decidability, definability and computability in number theory

ag.algebraic-geometry lo.logic nt.number-theory
Start Date
2020-08-17 
End Date
2020-12-18 
Institution
MSRI 
City
Berkeley, CA 
Country
USA 
Meeting Type
research program 
Homepage
http://www.msri.org/programs/319 
Contact Name
 

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.

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