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Derived algebraic geometry is a generalization of algebraic geometry modeled on derived commutative rings, which introduces homotopy theory into the topic. This generalization is particularly nicely suited for finding out singularities on moduli areas and has come to play an necessary role in geometric illustration theory and mathematical physics. This course shall be an introduction to the subject with a spotlight of deformation principle and applications to moduli areas. It will be mostly self-contained, assuming just some familiarity with algebraic geometry and homological algebra. In this course we research partial differential equations appearing in physics, materials sciences, biology, geometry, and engineering. We will contact upon questions of existence, long-time behaviour, formation of singularities, pattern formation.
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The course will start with the fundamental Model theory of Fraisse structures and their limits and then continue with examine of Logic actions of those limits. The aim is to reach a stage the place structural Ramsey concept could presumably be used to review these actions. Set principle and its relations with different branches of mathematics. Topics from giant cardinals, infinitary combinatorics and descriptive set theory.
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