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Past events in this series

Tue, 11 Oct 2022

Evaluating germs at poles and locality

Sylvie Paycha
(Institute of Mathematics University of 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. The question then amounts to  extending the ordinary
evaluation at a point on holomorphic germs 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 on germs
of meromorphic germs in several variables  with a prescribed type of
(linear) poles and show that modulo a Galois type transformation, they
amount to a minimal subtraction scheme in several variables.
This talk is based on joint work with Li Guo and Bin Zhang.