Thematic programs 2021
Each calendar year Leonhard Euler International Mathematical Institute hosts thematic programs gathering recognized experts in the respective fields as well as early career researchers and postdocs to carry out investigations with a special emphasis on collaborative activities. Every program features a summer school as well as one or two conferences or workshops. The stays of the visitors and speakers are fully or partially financially covered by the Institute.
The themes of the programs are open to suggestion via the application process. The selection criteria for accepting a proposal are its scientific strength and the degree to which the program would benefit mathematical research and postgraduate training in the Russian Federation.
Geometric and Mathematical Analysis, and Weak Geometric Structures
March 23 – December 23, 2021
Organizers:
Alexander Borichev, Université AixMarseille
Pavel Mozolyako, SaintPetersburg University
Roberta Musina, Università di Udine
Matteo Novaga, Università di Pisa
Eugene Stepanov, PDMI RAS
Dario Trevisan, Università di Pisa
This thematic program will be focused upon two directions of current mathematical research that encompass several interconnected areas related to geometric measure theory (GMT) and function spaces theory:
 Shape optimization problems and geometric analysis: minimal surfaces (with respect to various notions of surface area/perimeter including nonlocal ones) and related problems, clusters of soap bubbles, problems with prescribed curvature, the Steiner problem and transportation networks, as well as applications of shape optimization in image analysis (e.g. MumfordShah problem and similar) and mechanics (e.g. eigenvalue or compliance optimization or ground states of Schrödinger equation).
 Weak geometric structures related to GMT, such as currents, as well as those arising in optimal mass transportation and the study of geometry of highly irregular metric measure spaces, in particular those without any differentiable structure, with applications to the analysis of PDEs with very low regularity (e.g. weak and/or or probabilistic notions of flows, or “differential equations” with “purely nondifferentiable”, for instance just Hölder continuous unknowns, like those in Rough paths theory) and to some modern harmonic analysis problems.
 Purely geometric problems involving weak geometric structures, like extensions of Frobenius theorem either to irregular differential forms or distributions of planes or to weaker notions of surfaces like De Rham currents; extensions of ChowRachevsky theorem to irregular vector fields or flows; applications to subRiemannian geometry, geometric control theory and dynamical systems.
 Function spaces, especially Banach and Hilbert spaces of holomorphic and/or harmonic functions on the unit disc and polydisc: problems related to the geometry of such spaces and their invariant subspaces (e.g. cyclicity and hypercyclicity, shift operators), fine boundary behavior of their elements (e.g. harmonic measure and integral spectra estimates), related discrete models on trees and products of trees, timefrequency analysis and Gabor systems.
 Problems of potentialtheoretic nature, such as condensers, their capacities and their asymptotical behavior; fine properties of Cantortype sets on the plane e.g. Buffon needle with connections to combinatorics and Fourier analysis, Bessel capacity estimates for selfsimilar sets; properties of potentials on directed graphs; interpolation and sampling in function spaces on the unit disc; approximation problems in several complex variables.
The idea is to explore the deep connections between the above mentioned areas of research and to make them more comprehensible and attractive to both international and local mathematical
community.
The program includes the following minicourses:
 “Geometric flows of networks” by Matteo Novaga (Università di Pisa) and Alessandra Pluda (Università di Pisa), March 23 – April 1, 2021
 “Loops and Bubbles” by Roberta Musina (Università di Udine), April 13 – April 21, 2021
 “Gabor analysis for rational functions” by Yurii S. Belov (St. Petersburg State University), April 14 – May 26, 2021
 “Onedimensional optimization problems” by Emanuele Paolini (Università di Pisa), May 11 – May 19, 2021

“Makarov’s law of the iterated logarithm and integral means spectrum” by I.R. Kayumov (Kazan Federal University), June 25 – July 07, 2021 (in Russian)

“Several Complex Variables: Outline” by Norm Levenberg (Indiana University Bloomington), September 28 – October 28, 2021

“Condenser capacities: asymptotic formulas and geometric transforms” by V.N. Dubinin (IAM, Far East branch of the Russian Academy of Sciences), October 20 – October 29, 2021 (in Russian)

“Interpolation in Reproducing Kernel Hilbert Spaces” by Nikolaos Chalmoukis (Università di Bologna), November 17 – November 26, 2021

“Mean values of Riemann zeta function” by Winston Heap (Shandong University), November 17 – November 19, 2021

“The Hardy space in engineering” by Nicola Arcozzi (Università di Bologna), November 23 – November 25, 2021

“Geometry of the unit ball in various holomorphic spaces” by Konstantin Dyakonov (ICREA and Universitat de Barcelona), November 25 – December 2, 2021

“Large index subspaces in Banach spaces of analytic functions” by Alexander Borichev (Université AixMarseille), December 15 – December 18, 2021
The program also includes:

the conference “30th St.Petersburg Summer Meeting in Mathematical Analysis“, July 1 – 6, 2021

the school “Complex analysis, Combinatorics and Operator theory”, November 29 — December 3, 2021
Moduli Spaces, Combinatorics and Poisson Geometry
November 2021 – August 2022
Organizers:
Dmitry Korotkin, Concordia University and Centre de Recherches Mathématiques
Peter Zograf, PDMI RAS and St. Petersburg University
Moduli spaces have many nontrivial connections to other areas of mathematics: combinatorics, dynamics, integrable systems and Poisson geometry, to name a few. Among most celebrated results over the last 30 years one can mention several proofs of Witten’s conjecture about intersection numbers of ψclasses (Kontsevich, Mirzakhani and others), computation of Euler’s characteristics of moduli spaces (HarerZagier), development of the higher Teichmüller theory (Fock, Goncharov) and its links with cluster algebras and associated Poisson structures (Fomin, Zelevinsky). The research problems central for the program are:
 Establishing a relationship between meandric systems (pairs of transversal multicurves) on higher genus surfaces and squaretiled surfaces.
 Study of the large genus asymptotics of the numbers of meandric systems of given topological type.
 Computation of MasurVeech volumes of lower dimensional strata in the moduli space of quadratic differentials.
 Obtaining a relation of the distribution of geodesic multicurves to MasurVeech volumes.
 Establishing a relation between Joyce’s structures by Bridgeland to Frobenius manifolds and topological recursion formalism.
 Description the complete WKB expansion of the generating function of monodromy symplectomorphism for second order differential equations on Riemann surfaces with second order poles
and establishing the link to topological recursion formalism.  Application of the WKB formalism to general isomonodromic taufunction and embed it into the topological recursion framework. Generalization to higher genus using the formalism of Krichever and BertolaMalgrange.
 Construction of the dilogarithm line bundle over SL(2, R) cluster variety associated to the canonical symplectic form over the moduli spaces of bordered Riemann surfaces; description of the BohrSommerfeld symplectic leaves and their quantization.
The following activities will be organized during the program:
 school “Moduli Spaces, Combinatorics and Integrable Systems“, November 15 – 26, 2021
 conference “Combinatorics of Moduli Spaces, Cluster Algebras and Topological Recursion“, June 13 – 17, 2022
 [CANCELLED] conference “Geometry and Dynamics of Moduli Spaces“, August 1 – 5, 2022
 a number of minicourses given by invited visitors.
Spectral Theory and Mathematical Physics
February 1 – December 31, 2021
rescheduled from 2020 due to COVID19 pandemic
Organizers:
Alexander Fedotov, SPbU
Nikolai Filonov, PDMI
Alexander Its, IUPUI and SPbU
Alexander Sobolev, University College London
Tatiana Suslina, SPbU
Dmitri Yafaev, University of Rennes 1 and SPbU
The program is devoted to spectral theory and its applications. The spectral theory is one of the domains where the Saint Petersburg mathematical school is traditionally very strong, the names of L.D. Faddeev, M.S. Birman and V.S. Buslaev are among the names of the worldknown leaders in the field.
The following activities will be organized during the program:
 warmup online minicourses, November 2 – 26, 2020
 Seminar in Spectral Theory and Related Topics, February – December, 2021
 Seminar in Mathematical Physics, February – December, 2021
 conference “Asymptotic Methods in Mathematical Physics”, June 20 – 22, 2021
 St. Petersburg Conference in Spectral Theory, June 23 – 26, 2021
 Summer School in Spectral Theory, June 27 – 30, 2021
 a number of minicourses given by invited visitors.
New Trends in Mathematical Stochastics
August 15 – December 31, 2021
rescheduled from 2020 due to COVID19 pandemic
Organizers:
Ildar Ibragimov, PDMI
Yana Belopolskaya, SPbUACE
Andrei Borodin, PDMI
Yury Davydov, SPbU
Mikhail Lifshits, SPbU
Maria Platonova, PDMI and SPbU
Natalia Smorodina, PDMI and SPbU
Yuri Yakubovich, SPbU
Andrei Zaitsev, PDMI
Dmitry Zaporozhets, PDMI
The general idea of the program is to strengthen interactions between experts and young researchers working in the areas of probability theory, stochastic processes and their applications. Visits of leading scientists in these areas will serve to enrich the mathematical education in St. Petersburg and to develop possibilities for future collaboration.
The following activities will be organized during the program:
 introductory online school “Randomness online“, November 4 – 8, 2020
 conference “New Trends in Mathematical Stochastics”, August 30 – September 3, 2021
 workshop “St. Petersburg Youth Conference in Probability and Mathematical Physics“, December 20 – 23, 2021
 a number of minicourses given by invited visitors.