https://itmp.msu.ru/en/mscgeom...

The course gives an extended introduction into supergeometry and its applications. Ideas and methods of super- and graded geometry play an important role in modern theoretical physics and mathematics. Supergeometry gives a concise and powerful language to describe a collection  of compatible structures, leading to applications in homological algebra, index theory, quantization of gauge systems and supersymmetry. In addition to thorough introduction into the foundations of the subject, the course will also consider various recent developments and applications.

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Lecture 1. Introduction. Idea of Superspace.

Lecture 2. Functional-Algebraic Duality.

Lecture 3. Supermanifolds. Morphisms of Supermanifolds.