Katharina Dupont: Definable Valuations on Dependent Fields

The next meeting of the seminar in Logic, Set Theory  and Topology will be held on Tuesday, October 30. Time is 16:00 – 17:30.

Place: seminar room 201 which is located in the building of Computer Science Department (not Math Dept)

Speaker : Katharina Dupont (University of Constance, Germany)

Title: Definable Valuations on Dependent Fields

Abstract:

For my PhD project I am working on the question:

“When does a dependent field admit a non-trivial definable valuation?”,

which is motivated by a conjecture of Shelah.

This question brings together valuation theory and model theory and we expect that any progress to this question will have an impact on both fields.

It is known that finite fields, algebraically closed fields, real closed fields are dependent fields which have no definable valuations and that for any prime $p$  $\mathbb Q_p$ is an example of a dependent field with a definable valuation.

In my talk I will give a short introduction to the topic of definable valuations.  I will then present a method which uses definable subgroups to find definable valuations on fields and talk about how this might be used to prove a conjecture about definable valuations on dependent fields on which I am currently working.