Gerbes in Renormalization and Quantization of Infinite-Dimensional Moduli Spaces

• Applicant: Dr. Markus Upmeier
• Subject Area: Mathematics
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 339870907

Renormalization is a fundamental problem in the study of infinite-dimensional moduli spaces in order to extract meaningful quantities from these. In the considered cases (Yang-Mills theory, holomorphic curves) zeta regularization allows the construction of the Quillen metric on the determinant line bundle. The present project sketches an alternative approach to these metrics, which in the case of holomorphic curves are then compared to recent advances in the theory of elliptic genera.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2026: Geometry at Infinity
• International Connection: United Kingdom