November 7th, 2022

Time: 16:15-17:45

Location: Mondi 2

Speaker: Morris Brooks (Seiringer group)

Title: Effective Theories in Many Body Quantum Physics

Abstract: We will first review the well-established fact, that classical physics (depending on the context also referred to as Hartree / Gross-Pitaevskii / Landau-Pekar theory) arises as an effective theory in Many Body Quantum Physics, given that the number of particles goes to infinity. In the second part I want to discuss a recent result of Robert Seiringer and myself, where we confirmed a conjecture by Landau and Pekar from 1948, which claims that the energy-momentum relation of an electron moving in a polarized medium is asymptotically the same as the one of a free particle with an increased mass, and the increased mass is given by m=\alpha^4 m_{LP}+o(\alpha^4), where \alpha is the interaction strength between the electron and the polarized medium and m_{LP} is an explicit constant. In order to understand this conjecture, it is essential to use the Landau-Pekar theory as an effective theory for the polarized medium.

Speaker: Jakub Löwit (Hausel group)

Title: Finite and infinite fields in algebraic geometry

Abstract: In my talk, I would like to explain how one can relate "geometric" questions over complex numbers with "discrete" questions over finite fields. Surprisingly, it is often possible to answer complicated problems on one side using the other - one elegant manifestation of this principle is the famous Ax-Grothendieck theorem.