Oberseminar Mathematische Physik

Jointly with Johannes Alt (Bonn), Margherita Disertori (Bonn), Luca Fresta (Bonn) and Eveliina Peltola (Bonn & Aalto), I am co-organizing a mathematical physics seminar which takes place a few times per semester. The seminar usually takes place on Mondays from 2.15 - 3.15 pm in seminar room 0.006 (Endenicher Allee 60). 

Talks Spring 2024: 

• March 11, 2024: Théo Pinet (IMJ-PRG, Université Paris-Cité, UdeM)
  
  Existence of inflations for representations of shifted quantum affine algebras

  It is well known that the only simple finite-dimensional Lie algebra admitting a 2-dimensional irreducible representation is sl(2). The restriction functors arising in classical Lie theory, from inclusions of Dynkin diagrams, are therefore not essentially surjective on finite-dimensional simple modules. This talk aims to specify whether or not this surjectivity defect remains in the setting of Finkelberg-Tsymbaliuk’s shifted quantum affine algebras (SQAs for short).

  SQAs are infinite-dimensional algebras parametrized by a finite-dimensional Lie algebra and a coweight of this Lie algebra. They are natural variations of the usual quantum loop algebras which are in turn algebras of critical importance in geometry, in quantum integrable systems and in the study of cluster algebras. In this talk, we will give a pedagogical introduction to the remarkable representation theory of SQAs and will state an existence theorem for some notable modules, that we call inflations. We will construct these modules as special preimages for natural restriction functors (associated to inclusions of Dynkin diagrams) and will discuss important applications of their existence to the study of monoidal categorifications of cluster algebras and to integrable systems.

• April 15, 2024: Per Moosavi (Stockholm University)
  
  Anisotropic quantum Hall droplets

  I will discuss recent work on 2D droplets of non-interacting electrons in strong magnetic fields, confined by an anisotropic trapping potential. Using semiclassical methods, we obtain the one-particle energy spectrum and wave functions in the lowest Landau level by deriving and solving a transport equation inspired by standard WKB theory. This shows that energy eigenstates are localized on equipotentials of the trap, generalizing the rotational-symmetric situation for isotropic traps. From these microscopic first-principle considerations, we obtain explicit results for many-body observables for anisotropic quantum Hall droplets in the thermodynamic limit. In particular, we show that correlations along the droplet's edge are long-ranged, in agreement with low-energy edge modes described by a free chiral conformal field theory in terms of the canonical angle variable of the trapping potential.

• June 3, 2024: Arnaud Triay (LMU Munich) 

  tba