Evaluating germs at poles and locality

29.01.2021, 11:00  –  Online Seminar
Arbeitsgruppenseminar Analysis

Sylvie Paycha (Uni Potsdam)

How to evaluate  meromorphic germs at their poles while preserving a locality principle reminiscent of locality in QFT is a question that lies at the heart of  pQFT. It further  arises in other disguises in number theory, the combinatorics on cones and toric geometry. We introduce an abstract notion of locality and a related notion of mutually independent meromorphic germs in several variables. Much in the spirit of Speer's generalised evaluators in the framework of analytic renormalisation, the question then amounts to extending the ordinary evaluation at a point  to  certain algebras of meromorphic germs, in such a way that the extension factorises on mutually independent germs. In the talk, we shall describe a family of such extended evaluators  and show that modulo a Galois type  transformation, they amount to a minimal subtraction scheme in several variables.
This talk is based on ongoing joint work with Li Guo and Bin Zhang.

If you wish to attend the talks,  please contact Sylvie Paycha paycha@math.uni-potsdam.de for the login details.