Roughly speaking, representation theory studies abstract algebras by representing their elements a, b by matrices A, B and concretizing an abstract operation such as a+b by the corresponding operation A+B on matrices. The theory is applied in many areas of mathematics and physics. This bachelor thesis is a preparation for a later master thesis on algebraic operads.
This article is based on the Master thesis of the Faculty of Science, Engineering and Medicine of the University of Luxembourg, which was awarded the Germain Dondelinger Prize 2022, given each year by the “Amis de l’Université du Luxembourg” to one Master student from each of the three faculties of the university.
The work is located at the interface between geometry and particle physics. It deals with supergeometry or geometry of supersymmetry, i.e., the geometric framework for a symmetry that assumes that for every elementary particle of the Standard Model there exists a supersymmetric partner particle.
Derived Algebraic Geometry over Differential Operators
So far we supervised seven doctoral theses, five of which were accepted with the grade excellent (summa cum laude).
The following link leads to one of the six chapters of a recently defended dissertation on derived algebraic geometry over differential operators. The chapter was published in a rank A international journal of mathematical sciences.
