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Derived algebraic geometry is a generalization of algebraic geometry modeled on derived commutative rings, which introduces homotopy concept into the topic. This generalization is especially well suited for finding out singularities on moduli areas and has come to play an necessary role in geometric representation theory and mathematical physics. This course shall be an introduction to the topic with a spotlight of deformation principle and purposes to moduli spaces. It will be principally self-contained, assuming just some familiarity with algebraic geometry and homological algebra.

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