Model theory and applications

The aim of the course is to present applications of model theory (a branch of Mathematical Logic) in one or more area of mathematics. The particular direction will be determined by coordination with the students, but might include the following:

• Algebraic theory of differential equations (Galois theory, dimension, classification in dimension 1)
• Model theory of valued fields (imaginaries, integration theory, analytic spaces)
• o-minimality, with applications to arithmetic
• Difference fields and difference equations, applications to dynamics, asymptotic theory of the Frobenius
• Continuous model theory, applications to operator algebras, probability etc. Background from logic and other relevant areas will be covered as necessary.