Title: Variations on Locality
Speaker: Sylvie Paycha
Institution: University of Potsdam
Date & Time: August 24, 2024, 11:00–13:00
Location: Seminar Room 5, Mathematics Building, Jilin University
In quantum field theory, the principle of locality asserts that an object is directly influenced only by its immediate surroundings. We introduce
locality relations—defined as symmetric binary relations—that capture the essential features of this principle. Correspondingly, we define
locality morphisms, i.e., maps that factorize over products of pairs in the graph of such locality relations. This factorization property is pivotal in renormalization, which initially motivated our study of locality.
We demonstrate the utility of this framework in counting lattice points within a cone. This a priori infinite cardinal can be naturally renormalized via multivariate regularization, where locality plays a critical role in excluding "fake" finite contributions. It enables a
multivariate minimal subtraction scheme to isolate a meaningful finite part from the infinite cardinal. Joint work with Li Guo and Bin Zhang.
Sylvie Paycha has been a Professor in the Department of Mathematics at the University of Potsdam, Germany, since 2011, following a professorship at the University Clermont-Auvergne, France. She earned her PhD from Ruhr University Bochum. Her research in mathematical physics employs tools from pseudo-differential analysis, geometry, and number theory, with a focus on renormalization, zeta-function regularization, and their applications to quantum field theory and geometric analysis.
