International Conference. F.Delgado – ＂On Poincaré series of valuations on subfields of ..

Описание

International Conference, dedicated to the 75th birthday of Sabir M. Gusein-Zade
16.08.25
F. Delgado (Valladolid, Spain)
On Poincaré series of valuations on subfields of complex numbers

Earlier, there was defined and computed the Poincaré series in several contexts, all of them in the complex case. In two recent papers we give definitions of the Poincaré series of a collection of valuations in the real setting (i. e., on the ring of germs of functions on a real analytic variety), compute them for the case of one curve or divisorial valuation on the plane and discuss some of their properties. Recently, we have extended the computations to the case of other subfields of the complex numbers for one curve or divisorial valuation.

The talk will focus on the case of a single valuation, pointing out the differences with the well-known case of branches over algebraically closed fields, as well as the qualitative difference between the semigroup and the Poincaré series.

The results have been obtained in collaboration with S. Gusein-Zade and A. Campillo.

General information
The conference will be held in the Faculty of Mathematics of the HSE University (Usacheva str. 6, Moscow).
Dates: 16 - 20 June 2025
Organizers: A. Buryak, V. Medvedev, A. Skripchenko

More information:
https://math.hse.ru/modern_aspects_singularity_theory25/
https://mccme.ru/ru/modern_aspects_singularity_theory2025/

Автор

Mathematics at HSE