# Mathematical Sciences Research Institute

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# Seminar

DDC - Valuation Theory: Groups definable in difference-differential fields September 09, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program: Decidability, definability and computability in number theory: Part 1 - Virtual Semester MSRI: Online/Virtual
Speaker(s) Zoé Chatzidakis (École Normale Supérieure)
Description

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Video

#### Groups Definable In Difference-Differential Fields

Abstract/Media

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

In the context of a differentially closed field U of characteristic 0 with m commuting derivations (DCF_m) Phyllis Cassidy showed that if a group G is definable, contained in H(U), and Zariski dense in H where H is a simple algebraic group, then in fact G is conjugate to H(L), where L is "a field of constants".

With Bustamante and Montenegro, we generalize this to the context of DCF_mA, i.e., one adds a generic automorphism. The statement is a little different, since there are other fields around (Fix(\sigma) for instance), but similar. All definitions will be given, do not be scared by the apparently technical terms of the abstract.

 Notes 177 KB application/pdf

#### Groups Definable In Difference-Differential Fields

 H.264 Video 25139_28637_8487_Groups_Definable_in_Difference-Differential_Fields.mp4