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Explore the fundamental concepts of differential Galois theory in this mathematical seminar lecture from the Institute for Advanced Study. Learn about differential Galois groups as algebraic groups that describe symmetries of differential equation systems, with solutions existing in any differential field. Discover the natural framework of differentially closed fields for studying such symmetries and follow a sketch of the proof for the fundamental theorem of differential Galois theory. Examine Kolchin's geometric approach to differential equations and gain insights into the Hrushovski-Sokolovic classification of strongly minimal differential equations, which serve as building blocks for all differential equations in differentially closed fields.
