# Semyon Klevtsov

## Biography - Semyon Klevtsov

### Institute for Advanced Mathematical Research (IRMA), University of Strasbourg and CNRS

Semyon Klevtsov obtained his PhD in mathematical physics in 2009 at Rutgers University (USA). After a post-doctoral fellowship at the Free University of Brussels (Belgium) he has, since 2012, held the positions of Humboldt postdoctoral fellow and, subsequently, principal investigator at the Mathematical Institute of the University of Cologne, funded by the German Science Foundation (DFG). During his time there, he received the 2015 Max Delbrück prize for junior researchers. In 2019, he joined the Institute for Advanced Mathematical Research (IRMA) at the University of Strasbourg, as professor of mathematical physics.

His research interests focus on modern mathematical physics, and include random metrics and random surfaces, Bergman kernels, Kahler geometry and geometric methods in physics, in particular in quantum mechanics and quantum field theory. More recently, he has been interested in mathematics of the strongly correlated electron systems in condensed matter physics.

## Project - Geometry of Quantum Hall States

### 01/09/2020 - 31/08/2022

Quantum Hall effect (QHE) is a remarkable phenomenon, which occurs in certain two-dimensional electron systems subjected to low temperatures and strong magnetic fields. In essence, the Hall conductance in these situations takes on quantised values, i.e., integer or fractional values with a very high precision, exceptional for materials with impurities. Since its discovery in the 1980s, the quantum Hall effect continues to fascinate scientists, as an example of a physical system, where quantum effects can be observed macroscopically. Applications of QHE systems vary from precision metrology to potential platforms for quantum computing.

The aim of this project is to develop the geometric theory of the N-particle wave functions, describing the correlated electronic states in the quantum Hall effect. Since the early pioneering work on the theory of QHE by Laughlin, Thouless, Simon and later work by Haldane, Bellissard, Fröhlich, Avron-Seiler-Zograf, Read, Wen, Wiegmann and others — it was understood that the explanation for the quantum Hall phenomena is essentially geometric in nature. The goal of this project is to further develop the mathematical side of this theory.

In particular, the plan is to address several important physics conjectures in the field, such as the topological degeneracy of quantum Hall states, tentative existence of the asymptotically projective flat adiabatic connection for the transport of the states on various parameter spaces, and existence of large N asymptotic limits. This project is at the intersection of modern mathematical physics, many-body quantum mechanics, geometry, analysis and probability. The main tools come from the geometry of Riemann surfaces, moduli spaces, holomorphic line bundles, Bergman kernels, Kahler geometry, Gaussian free fields. The expected outcome of the project is to uncover new exciting connections of the QHE states with various aspects of modern geometry and physics.

## Post-doc biography - Thibaut Lemoine

### Institute for Advanced Mathematical Research (IRMA), University of Strasbourg and CNRS

After having studied finance at the EDHEC Business School in France, Thibaut Lemoine decided to specialise in pure and applied mathematics, with a stress on mathematical physics. He obtained a Bachelor’s degree, a Master’s degree and then a PhD in mathematics at the University Pierre and Marie Curie (UPMC), Paris - now known as Sorbonne University. His research at the intersection of probability, noncommutative harmonic analysis and the theory of surfaces enabled him to make significant contributions to two-dimensional Yang-Mills theory. In particular, he showed the convergence of Yang-Mills partition function with structure group SU(N) and U(N), when N goes to infinity, for compact surfaces of genus 1 and higher, as well as the convergence of the associated Wilson loops.

In October 2020, he obtained his PhD under the supervision of Professor Thierry Lévy (LPSM, Sorbonne University), and subsequently joined the University of Strasbourg as a postdoctoral researcher for the project “Geometry of Quantum Hall States” initiated by Semyon Klevtsov, which addresses the mathematical aspects of Quantum Hall effect (QHE).

## Links

- Semyon Klevtsov's web page
- Colloquium Physique et Mathématique : "Quantum computing and Quantum information"
*(24/06/21)* - Conference: Mathematical aspects of quantum phases of matter, Będlewo, Poland
*(18-25/07/21)* *C*olloquium Physique et Mathématique : “Many-body localization"*(06/12/2021)*