The objective of the project is the development of modern directions in mathematical analysis at the Saint Petersburg State University. We expect to review new interrelations between possibility theory and analysis that arise in the study of determinantal processes and areas associated with them and their connection with conformal field theory. The main research topics and tasks are:
 Determinantal processes arising from physical models. We expect to study determinantal processes on a plane and analyse corresponding correlation kernels. We will study the behaviour of a model of a Coulomb gas near the spectral boundary and the behaviour of models with higher Landau levels (polyanalytic Ginibre ensembles).
 The inverse problem of potential theory and Schwartz functions. In the classical normal random matrix model, we expect to study the equilibrium measures of the ensemble of the corresponding Coulomb gas. We are planning to use complex dynamics methods to answer some fundamental questions related to the shapes of drops (carriers of equilibrium measures) as well as their change when the potential changes (for example, Laplacian growth).
 The research in the field of the uncertainty principle in harmonic analysis. This area includes problems of the completeness of exponentials and polynomials formulated by Wiener and Kolmogorov over 70 years ago, inverse spectral problems of differential operators and Krein canonical systems, the theory of de Branges spaces of entire functions, classical problems of the theory of stationary Gaussian processes, problems of signal processing etc., as well as their modern generalisations and applications.
 The development of a perturbation theory for linear operators. The goal of this part of the project is the research of the question of the extent to which perturbed operator functions can differ from the initial operator depending on the properties of perturbation and the function. Similar problems arise in the study of functions of several (switching and not necessarily switching) operators.
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International Laboratory of Cluster Geometry of the Faculty of Mathematics of the Higher School of Economics
Higher School of Economics — National Research University 
Maths 
Moscow 
Shapiro Michael
Russia 
20212023 
Laboratory of Interdisciplinary Power Engineering Problems
Ulyanovsk State Technical University 
Maths 
Ulyanovsk 
Simos Theodore Elias
Greece 
20212023 
Laboratory of Combinatorial and Geometrical Structures
Moscow Institute of Physics and Technology 
Maths 
Dolgoprudniy 
János Pach
Hungary, USA 
20192021 