Erik Walsberg


UC Irvine


Monday, February 1, 2021 - 4:00am to 5:30am



Model theory of fields is a very successful topic. I believe it is fair to say that most of this subject consists of detailed studies to particular fields (the reals, complex, p-adic, etc...). Largeness is a field-theoretic notion introduced by Pop in the nineties. This notion now plays a very important role in Galois theory and is increasingly being studied for other purposes. A number of people, including myself, have long believed that largeness should play an important role in the model theory of fields. This is mainly because all known model-theoretically tame fields are large, so one hopes that a general model-theoretic study of large fields might have a unifying effect on the model theory of fields. Over the past year we have begun to develop a model theory of large fields and in particular we have proven the stable fields conjecture for large fields. The key tool is a new topology on the K-points of a variety over a large field K.

This talk will involve a little algebraic geometry, but I will try to make it accessible to those with minimal background.