Model Theory and Algebra of Valued Fields

This is a graduate lecture course given jointly by Jochen Koenigsmann (Oxford) and Deirdre Haskell (McMaster). The schedule is roughly as follows:

Week 1 Basics on valuations and places
Week 2 Extensions and Henselian valued fields
Week 3 Model theory of valued fields, especially quantifier elimination results
Week 4 Topological aspects
Week 5 First-order definability of Henselian valued rings
Week 6 Local-global principles, regularly closed fields
Week 7 Galois theory of valued fields
Week 8 Quick look at Hilbert's tenth problem, anabelian geometry and/or the inverse Galois problem

Lectures are timetabled as follows:

    Weeks 1-2, 4-8, to be given by Jochen Koenigsmann on Wednesdays and Fridays at 10am in SR1. The algebraic aspects of the theory will be covered in these lectures. Week 3, to be given by Deirdre Haskell in 6 hours: Wednesday 10-12, Thursday 11-1, Friday 9 -11. These lectures will cover the model-theoretic aspects of the theory.

Lecture notes for the course will be posted and periodically updated (with inevitable corrections).

Lecture notes

 

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