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.

Список всех тем лекций

Lecture 1. Introduction. Idea of Superspace.

Lecture 2. Functional-Algebraic Duality.

Lecture 3. Supermanifolds. Morphisms of Supermanifolds.

Lecture 4. Supermanifolds and Their Maps.

Lecture 5. More on Supermanifolds and Their Maps.

Lecture 6. Further Differential Calculus.

Lecture 7. Final Remarks on Differential Calculus. Tensors on Supermanifolds.

Lecture 8. Berezin Integration.

Lecture 9. Supertrace and Superdeterminant.

Lecture 10. Berezinian (Axiomatic Approach, Relation with Supertrace).

Lecture 11. Final Remarks on Integrals. Differential Forms.

Lecture 12. More on Differential Forms.

Lecture 13. Pseudodifferential Forms. Multivector Fields. Integral Forms.