Two-dimensional local fields and integration on them (Ivan Fesenko, University of Nottingham)

25.09.2019 11:00

Two-dimensional local fields include formal loop objects such as $R((t))$, $C((t))$, $Q_p((t))$ and also fields such as $F_p((t_1))((t_2))$, $Q_p\{\{t\}\}$. They play the fundamental role in two-dimensional number theory, arithmetic geometry, representation theory, algebraic topology and math physics. I will explain basic things about such fields, including their unusual topology and the theory of measure and integration on such fields and Fourier transform which can be viewed as a (rigorous) arithmetic version of the Feynman integral. While one-dimensional local fields show up in tropical geometry of curves, one may expect that two-dimensional local fields should be involved in tropical geometry of surfaces.

Lieu

Bâtiment: Battelle

Villa Battelle, Séminaire "Fables géométriques"

Organisé par

Faculté des sciences
Section de mathématiques

Intervenant-e-s

Ivan Fesenko, University of Nottingham

entrée libre

Classement

Catégorie: Séminaire