Steffen Schmidt

July 22, 2025: Steffen Schmidt has today successfully defended his thesis "On Unitarity for $\mathfrak{sl}(m\vert n)$-Supermodules: Dirac Cohomology, Superdimension, Indices".

• Unitarity for Lie supergroups and Lie superalgebras; construction and classification.
• Dirac cohomology for Lie superalgebras.
• Infinite-dimensional representations of Lie supergroups, in particular tensor product decompositions, the Duflo-Serganova cohomology functor.
• Applications of representation theory in theoretical physics: Index theorems such as the Witten index or the Superconformal index.
• Factorization algebras in quantum field theories and their connection to unitary representations.