Aktuelles

Mittwoch, 20.12.2023: On the generalization of enumerative invariants of F_2

Parisa Ebrahimian (University of Tübingen)

Maxim Lvovich Kontsevich found a recursive formula for counting the number of complex plane rational curves of degree d that pass through general given points. These numbers are GW invariants for the plane. Hannah Markwig and Andreas Gathmann provided a completely combinatorial proof of Kontsevich’s formula by using tropical geometric methods. Tropical geometry is a development in algebraic geometry that aims to simplify algebro-geometric problems into purely combinatorial ones and it is used as a modern tool that can solve enumerative problems effectively. To successfully apply tropical geometry to an enumerative problem, a so-called correspondence theorem is required. In this talk, we are going to see a further generalization of Kontsevich’s formula to the case where the curves are in a Hirzebruch surface and they are required to satisfy not only point and line conditions but also multiple cross-ratio conditions.

Uhrzeit:	10:15 - 11:15
Ort:	S08
Gruppe:	Oberseminar kombinatorische algebraische Geometrie
Einladender:	Daniele Agostini, Hannah Markwig

Donnerstag, 21.12.2023: Effective polaron dynamics for an impurity particle interacting with a Fermi gas

Viet Hoang (Tübingen)

We study the quantum dynamics of a homogeneous ideal Fermi gas coupled to an impurity particle on a 3-dimensional box with periodic boundaries. For large Fermi momentum \kF, we prove that the effective dynamics is generated by a Fröhlich-type polaron Hamiltonian, which linearly couples the impurity particle to an almost-bosonic excitation field. Our method applies to the case of an interaction coupling \lambda=1 and time scales of order \kF^{-1}, allowing us to compare our results with experimental observations.

Uhrzeit:	14:30
Ort:	C3N14
Gruppe:	Oberseminar Mathematical Physics
Einladender:	Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka

Donnerstag, 21.12.2023: Many-body particle systems and their thermodynamic and semi-classical properties

Dr. Christiaan van de Ven (Universität Würzburg)

An overview of some of my previous research contributions is given. These deal with: a) the mathematical formalism of the classical limit of quantum theories; b) asymptotic emergence, i.e., the ability of a system to exhibit certain singular behavior in a certain limit of quantum theories. Special emphasis is given on spontaneous symmetry breaking and phase transitions, where the role of local perturbation theory is highlighted. c) large deviation principles in spin systems, including quantum spin tunneling and eigenfunction localization; d) equilibrium statistical mechanics, both from quantum and classical perspectives in which the classical KMS condition and its derivation play a central role.

Uhrzeit:	16:00
Ort:	C3N14
Gruppe:	Oberseminar Mathematical Physics
Einladender:	Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka