Gleb Kotousov

My research is focused on `integrable’ or `exactly solvable’ models in field theory and statistical mechanics. These turn out to have a surprising variety of applications and they are being actively studied by many research groups around the world. To date, new ideas from the field of integrable systems have had a profound impact on many areas of modern mathematics including algebra, topology, geometry and mathematical analysis. In physics, integrable models describe real low dimensional statistical systems such as quantum gasses, which are starting to be realized in cold atom experiments; and have found applications in high energy physics and string theory. 

In my latest studies, I have been trying to better understand critical phenomena by analyzing the scaling limit of integrable, critical 1+1 dimensional quantum spin chains. We have developed a new mathematical approach to the problem, based on the so-called ODE/IQFT correspondence, which is significantly more powerful than any other analytic or numerical technique. The method has enabled us to obtained new results for `non-rational' CFTs, where the spectrum of critical exponents possesses a continuous component. Such models appear in string theory, within the AdS/CFT correspondence, and are expected to provide a theoretical description of condensed matter systems with disorder.

I have taught the Masters course `Quantum Field Theory' at Leibniz University Hannover during the Winter 2024/2025 semester.

I take part in the supervision of undergraduate and post-graduate students at both Leibniz University Hannover and Rutgers University.