Cohomological Field Theories secure successful dissertation

Published 02.08.2023

Congratulations also go to Shuhan Jiang on the successful dissertation defense. He is a researcher in the group of Jürgen Jost, who was his advisor for his great work on "Mathematical Structures of Cohomological Field Theories". All the best for your future!

Shuhan obtained his Bachhelor of Science in Physics at the Nankai University in China. Since 2018, he has been a member of the Geometry, Analysis, Theoretical Physics and Machine Learning group of Jürgen Jost, starting as a predoctoral fellow.  His current research interests include graded geometry and cohomological field theory. In the past, he also worked on quantum information theory, especially on Bell's nonlocality, multipartite entanglement, and quantum information processing.

This is how he describes his research in detail: "In this dissertation, we developed a mathematical framework for cohomological field theories (CohFTs) in the language of "QK-manifolds", which unifies the previous ones in (Baulieu and Singer 1988; Baulieu and Singer 1989; Ouvry, Stora, and Van Baal 1989; Atiyah and Jeffrey 1990; Birmingham et al. 1991; Kalkman 1993; Blau 1993). Within this new framework, we classified the (gauge invariant) solutions to the descent equations in CohFTs (with gauge symmetries). We revisited Witten’s idea of topological twisting and showed that the twisted super-Poincaré algebra gives rise naturally to a "QK-structure". We also generalized the Mathai-Quillen construction of the universal Thom class via a variational bicomplex lift of the equivariant cohomology. Our framework enables a uniform treatment of examples like topological quantum mechanics, topological sigma model, and topological Yang-Mills theory."