Introduction to Differential Galois Theory

Differential Galois groups are algebraic groups that describe symmetries of some systems of differential equations. The solutions considered can live in any differential field and thus a natural framework to consider such symmetries is the setting of differentially closed fields. I will describe this setting and sketch the proof of the fundamental theorem of differential Galois theory using it. If time permits, I will mention Kolchin's geometric approach to study differential equations, and Hrushovski-Sokolovic classification of strongly minimal differential equations (building blocks of all differential equations in differentially closed fields).