# A multivariable approach to renormalisation: Meromorphic germs with linear poles and the geometry of cones

### APA

Paycha, S. (2019). A multivariable approach to renormalisation: Meromorphic germs with linear poles and the geometry of cones. Perimeter Institute. https://pirsa.org/19110114

### MLA

Paycha, Sylvie. A multivariable approach to renormalisation: Meromorphic germs with linear poles and the geometry of cones. Perimeter Institute, Nov. 13, 2019, https://pirsa.org/19110114

### BibTex

@misc{ pirsa_PIRSA:19110114, doi = {10.48660/19110114}, url = {https://pirsa.org/19110114}, author = {Paycha, Sylvie}, keywords = {Other}, language = {en}, title = {A multivariable approach to renormalisation: Meromorphic germs with linear poles and the geometry of cones}, publisher = {Perimeter Institute}, year = {2019}, month = {nov}, note = {PIRSA:19110114 see, \url{https://pirsa.org}} }

Sylvie Paycha University of Potsdam

## Abstract

Analytic renormalisation "à la Speer" using a multivariable approach typically leads to meromorphic germs in several variables whose poles are linear. In particular, Feynman integrals, multizeta functions and their generalisations, namely discrete sums on cones and discrete sums associated with trees give rise to meromorphic germs at zero with linear poles. We shall present a multivariable renormalisation scheme which amounts to a minimal subtraction scheme in several variables. It preserves locality in so far as the evaluation at poles is expected to factor on functions with independent sets of variables. Inspired by Speer, we shall discuss a class of generalised evaluators that do the job. Using a theory of Laurent expansions on meromorphic germs with linear poles at zero, we shall relate these generalised evaluators to the geometry of cones.

This talk is based on joint work with Pierre Clavier, Li Guo and Bin Zhang.