Model Theory and Arithmetic

Abstract

The workshop “Model Theory and Arithmetic” brought together communities working in model theory (a subfield of mathematical logic) and in number theory, in particular arithmetic geometry. There has been a flurry of new ideas and results going back and forth between these areas recently. For example, o-minimality has been fruitfully used in Hodge theory and diophantine geometry, and model theoretic approaches to perfectoid fields and Arakelov geometry are emerging. Oberwolfach provided the ideal setting to gather these two groups in one place in order to facilitate the exchange of ideas between them. Talks covered a diverse range of topics, but common themes were tame geometry (also in non-archimedean settings) and transcendence questions.