Program
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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)
Tags/Keywords
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