Alexey Ovchinnikov : Difference closed pseudofields and difference Galois theory.

Posted by , part of the Logic Seminar.

At

Jan. 26, 2010, 4 p.m.

In

SEO 612

Abstract

In this talk, we apply Dima Trushin's work on difference Nullstellensatz for difference closed pseudofields to construct a Galois theory of difference equations with difference parameters. Existing Galois theories for difference and differential equations with differential parameters developed by Cassidy, Singer, and Hardouin are based on differentially closed fields. However, in our case difference closed fields are not a valid substitute due to their lack of quantifier elimination, and, therefore, we are using difference simple rings that are products of fields (called pseudofields) instead.

seminar begins with tea.