Arithmetic Analysis

by Prof. Alexander Goncharov (Yale University)

Tuesday 21 Jun 2022, 17:00 → 18:00 Europe/Berlin

H4 (Geomatikum)

Historically, a large part of Algebraic Geometry was developed  by  Abel -  Riemann - Jacobi - ...  to understand the properties of integrals.I will explain new methods which allow to make precise predictions about a wide class of integrals without calculating them. These  methods, which sound quite elementary,  are based on deep ideas of the arithmetic theory of motives, such as motivic Galois groups, originated by Grothendieck, Deligne, Beilinson, ... 

Application of arithmetic analysis to the simplest kinds of iterated integrals revealed surprising connections to the geometry of modular curves and more generally locally symmetric spaces.During the last 10+ years, arithmetic analysis was successfully used to understand/calculate scattering amplitudes in  Quantum Field Theory. It is likely that it will become a part of the mathematical structure describing QFT's. 

Zoom Link: https://uni-hamburg.zoom.us/j/63441868540?pwd=N2xjUktiLy9hOE9nTjFCMUx3UXFPdz09