Supergeometry and applications in physics

[MathematicalPhysicist]

I would like to know what are the prequisites for a graduate course with a handle "supergeometry and applications in physics", Iv'e read somewhere that it uses a lot of algebraic geometry, schemes, I guess that after the lecturer will publish the syllabus with the prequisites, I'll be wiser, nontheless I would like to know form others well versed in this topic which is obviously under 'mathematical physics'.

 

[Finbar]

I would like to know what are the prequisites for a graduate course with a handle "supergeometry and applications in physics", Iv'e read somewhere that it uses a lot of algebraic geometry, schemes, I guess that after the lecturer will publish the syllabus with the prequisites, I'll be wiser, nontheless I would like to know form others well versed in this topic which is obviously under 'mathematical physics'.

I would say an undergraduate degree in mathematics or theorectical physics with some knowledge of differential geometry and/or relativistic field theory. Probably some understanding of group theory supersymmetry is an extension of the Poincare symmetry group. I'd guess you'd want to have taken some more basic graduate coarses in geometry applications to field theory before this coarse.

 

[Entropia]

Supergeometry is a branch of mathematics that deals with the generalization of geometry to include both commuting and anticommuting coordinates, known as "supercoordinates." It has many applications in physics, particularly in the study of supersymmetry and supergravity.

In order to take a graduate course on supergeometry and its applications in physics, it is likely that a strong background in algebraic geometry and schemes will be necessary. This is because supergeometry uses many concepts and techniques from these areas of mathematics.

Specifically, students should have a solid understanding of commutative algebra, including topics such as modules, homological algebra, and sheaf theory. They should also be familiar with algebraic varieties and schemes, as well as their associated concepts of morphisms, sheaves, and cohomology.

Additionally, a background in differential geometry and Lie theory would be beneficial, as supergeometry also involves the study of supermanifolds and super Lie groups.

It is also important to have a good grasp of mathematical physics, including quantum mechanics and field theory, as these are the areas where supergeometry finds its most significant applications.

Of course, the specific prerequisites for a course on supergeometry and its applications in physics will depend on the individual instructor and the focus of the course. However, a strong foundation in the aforementioned areas of mathematics and physics will likely be necessary for success in such a course.