# Математический центр «Сириус»

English version

## О центре

Математический центр «Сириус» (SMC) учрежден в 2019 году Образовательным фондом «Талант и Успех» для проведения научных исследований в области математических наук и школ для молодых ученых. Центр использует Олимпийское наследие в Сочи, располагается и проводит мероприятия в гостинице «Омега Сириус Парк» возле Олимпийского парка на побережье Черного моря.

### Миссия

Центр ставит своей целью активизацию математических исследований в России, а также расширение сети личных и профессиональных контактов между математиками. Мы стремимся стать местом встречи исследователей в области математики для обмена научными идеями, совместной работы, профессионального роста студентов и молодых ученых.

### Научный совет

Научный совет центра устанавливает критерии отбора заявок на проведение мероприятий, оценивает заявки и составляет научную программу. В настоящий момент его членами являются

• Мария Х. Эстебан (CEREMADE, CNRS & Université Paris-Dauphine)
• Сергей Ландо (Высшая школа экономики & Сколковский институт науки и технологий)
• Арий Лаптев (SMC, директор; Imperial College London)
• Алексей Щуплев (SMC, заместитель директора)
• Август Цих (Сибирский федеральный университет, Красноярск).

### Деятельность

Центр проводит регулярные мероприятия в рамках трех видов активностей: недельных конференций, школ для молодых исследователей и встреч исследовательских групп. Подробнее о форматах работы и условиях можно прочитать здесь (на английском языке).

### Прием заявок

Центр принимает заявки для проведения недельных конференций, школ для молодых исследователей и встреч исследовательских групп в 2021. Заявки принимаются до 6 сентября 2020. Рекомендации для составления заявок здесь (на английском языке).

## Будущие мероприятия

Все конференции и школы центра открыты для всех желающих. Однако, если вы планируете посетить мероприятие, собщите нам об этом заранее.

### Конференции

004w: Complex Approximations, Orthogonal Polynomials and Applications, перенесена на 2021

Описание: The goal of the workshop is to bring together leading experts to discuss the latest achievements in the area of complex approximations and orthogonal polynomials. The main direction of the workshop is to communicate recent results in the theory of rational approximation of analytic functions. Important tools for rational approximation are the Riemann-Hilbert problems, the theory of orthogonal polynomials, the theory of the logarithmic potential and the operator theory for difference operators. The main objective of the workshop is to discuss the applications of complex approximations and orthogonal polynomials in the spectral theory of difference operators, random matrices models and special functions, which play an important role in applied and computational mathematics.

Организаторы: Alexander Aptekarev (Keldysh Institute of Applied Mathematics), Vladimir Lysov (Keldysh Institute of Applied Mathematics).

Внешний сайт: http://caopa2020.tilda.ws/

005w: Future and Emerging Mathematical Technologies for Innovations in Industry and Society, перенесена на 2021

Описание: The primary objective of the meeting is to discuss future and emerging mathematical technologies, and to share experience and best practices of organizing collaborative research projects with industry, as well as to discuss and brainstorm about joint future activities. One of the major obstacles to be addressed is the low visibility of mathematical technologies in European programs. Theerefore, an important objective is to discuss measures facilitating awareness about existing expertise in Europe and knowledge transfer. Another prime objective of this workshop is to discuss a strategic research agenda (SRA) for the mathematical sciences. The writing process for such SRA is currently being started up, and the workshop would be an ideal opportunity to discuss the SRA and its contents in detail. The workshop is organized under the auspices of EU-MATHS-IN – a European Network of Mathematics for Industry and Innovation. This network is a collaboration of national organizations from 20 European countries. The promoting partners of EU-MATHS-IN are the European Mathematical Society and the European Consortium for Mathematics in Industry.

Организаторы: Wil Schilders (Eindhoven University).

006w: Classical and Quantum Integrable Systems, перенесена на 2021

Описание: This workshop continues the series of CQIS workshops held in 2004-2019 in Dubna, Protvino, Chernogolovka and St. Petersburg. The idea of the workshop is to bring together 70-100 mathematical physicists and mathematicians working in the field of integrable models and related fields. Traditionally, we anticipate strong participation of scientists from Russia and FSU countries. At the same time, we welcome scientists from all around the world and we expect that their participation will contribute considerably to the objectives of the workshop. The scientific scope of the workshop covers recent results in integrable models of classical and quantum mechanics, field theory and statistical physics, various algebraic, geometric and combinatorial aspects of integrability including quantum algebras and quantum groups, cluster algebras, conformal field theory, W-algebras etc, integrable probability and asymptotic representation theory.

Организаторы: Sergei Lando (HSE University), Andrey Pogrebkov (Steklov Mathematical Institute), Alexander Povolotsky (Joint Institute for Nuclear Research), Pavel Pyatov (HSE University), Pavel Saponov (HSE University).

007w: Integrable Systems and Their Applications, перенесена на 2021

Описание: The purpose of the conference is to establish international contacts for the subsequent involvement of world experts in cooperation with Russian scientists in the field of geometry and topology, dynamical systems, as well as other related areas of mathematics.

Организаторы: Huijun Fan (Peking University), Andrey Mironov (Sobolev Institute of Mathematics), Iskander Taimanov (Sobolev Institute of Mathematics), Youjin Zhang (Tsinghua University), Jian Zhou (Tsinghua University).

008w: Lower Bound in Computational Complexity, перенесена на 2021

Описание: The aim of the workshop is to bring together researchers working on algorithms and complexity theory to discuss recent progress on these questions including new techniques for proving lower bounds and connections to other fields including: circuit complexity (what is the minimum number of basic operations needed to compute a given function?), proof complexity (what is the minimum number of steps needed to prove a given tautology?), communication complexity (what is the minimum amount of information that two or more parties need to exchange in order to compute a given function?), fine-grained complexity and conditional lower bounds (what is the minimum running time exponent for algorithms computing given functions, and what relationships exist between the running times for different functions?).

Организаторы: Alexander Kulikov (PDMI RAS), Ryan Williams (MIT).

009w: Complex Analysis and Spectral Theory, перенесена на 2021

Описание: The conference will bring together leading experts in complex and functional analysis who are working in the area of approximation theory, on gap and density, sampling and interpolation problems in various spaces of analytic functions, as well as on their applications to spectral theory, harmonic analysis, and random analytic functions. We will explore new advances in these areas emphasizing the interplay between complex function theory, harmonic analysis, and operator theory on the one side, and mathematical physics and probability on the other. We hope to be able to state some new ambitious fundamental problems, and to brainstorm various ideas for solving them. The conference will initiate new exciting interactions and collaborations between groups of participants. The participation of young researchers will be especially encouraged.

Организаторы: Ujue Etayo (TU Graz), Håkan Hedenmalm (KTH), Nikolai Makarov (Caltech), Alexei Poltoratski (University of Wisconsin-Madison), Roman Romanov (St. Petersburg University).

010w: Variational Methods in Nonlinear Nonlocal PDEs, перенесена на 2021

Описание: This workshop will focus on recent developments of mathematical analysis tools and variational methods in some selected new applications of the field of nonlinear nonlocal aggregation/diffusion PDEs. Kinetic modelling typically concentrates on situations which can be identified, at the modelling stage, as systems made out of a large number of individuals showing a collective behaviour. The main question is how to obtain from them averaged information. The behavior of individuals can be usually modelled via stochastic/deterministic ODEs from which one obtains mesoscopic and/or macroscopic descriptions based on mean-field type PDEs. The interplay between the aggregation/interaction behavior (nonlocal, nonlinear), the transport phenomena, and the diffusion, is the main goal of this workshop both at the stationary and the dynamical level.

Организаторы: José Antonio Carrillo (Imperial College London), Lucia Scardia (Heriot-Watt University), Bruno Volzone (Università "Parthenope"), Yao Yao (Georgia Institute of Technology).

011w: Graph Complexes, Configuration Spaces and Moduli Spaces, отменена

Описание: The Graph Complex is at the crossroad of many exciting mathematical subjects. The aim of the conference is a deeper understanding of the connections between these subjects and exploring new ones. One of the first appearances of the Graph Complex was in the proof of the formality of the Lie algebra of Hochschild cohomology of polynomials by Maxim Kontsevich. In this proof an explicit $L_\infty$ morphism was constructed. It contains non-trivial integrals, which are essentially multiple zeta values. While working on the independent proof of formality conjecture Dmitry Tamarkin noted, that one has not only one formality but a bunch of them. These formalities are acted by the Grothendieck-Teichmüller group, which was introduced by Drinfeld in 1991, following earlier ideas of Deligne-Grothendieck. Later on, in his seminal work, Wilwacher showed, that the both Grothendieck-Teichmüller group and set of formality are managed by the Graph complex. It means, in particular, that the 0-th cohomology of the Graph complex equals to the Grothendieck-Teichmüller group. It establishes a surprising relation between the Graph Complex and the Grothendieck-Teichmüller group. In further papers of Willwacher, Turchin, and others, it was shown, that the Graph complex and its modifications calculate the space of maps between little disks operads of different dimensions and describe models of configuration spaces as well. This is consistent with the action of Grothendieck-Teichmüller group action on the operad of little disks, which was, in a nutshell, the motivation of the initial definition of Drinfeld-Deligne-Grothendieck. One of the late appearances the Graph Complex made in the paper of Galatius and coauthors. They showed, that the weight zero part of cohomology of moduli spaces of stable curves is given by the Graph complex. This intriguing result is still waiting to be connected with diverse incarnations of the Graph Complex.

Организаторы: Anton Khoroshkin (HSE University), Nikita Markarian (HSE University)

012w: Multidimensional Residues and Tropical Geometry, Nov 29 - Dec 5, 2020

Описание: Integral representations and residues is a powerful tool for studying functions and computing integrals. By integrals one can represent a number of solutions of a system of equations, the roots, solutions to differential equations, many special functions of mathematical physics. As a rule, construction of residues is closely related to analytic sets; therefore, the residue theory goes deep into algebraic geometry, in particular in the problem of ideal membership and the effective Nulstellensatz. In the last decades the ideas of the multidimensional residue theory proved to be useful in tropical geometry thanks to important notions of the Jensen-Ronkin counting function and of a supercurrent, which is related to the Monge-Ampere problem in the pluripotential theory. In the last decades the studies led to discovery of new regularizations of residue currents, Koppelman formulas for solution of a d-bar problem on analytic sets. There have been constructed residue currents associated to weakly holomorphic functions; a non-standard interpolation problem for holomorphic functions has been solved using the Grothendieck residues; a k-convexity (according to Gromov) for a complement of an amoeba for a complete intersection has been proved. The major topic for discussions during the proposed workshop are: k-convexity (according to Gromov) for complements of amoebas in case of incomplete intersections; tropical Hodge theory; tropical version of the Gelfond-Khovansky theorem; logarithmic Gauss mapping and non-standard interpolation in analytic spaces; computation of the Mellin-Barnes integrals with applications to mathematical physics.

Организаторы: August Tsikh (Siberian Federal University), Mats Andersson (Chalmers tekniska högskola och Göteborgs universitet).

### Школы

001s: Spectral and Functional Inequalities and Their Applications, postponed until further notice

Описание: We shall start with some preliminary material describing basic concepts of self-adjoint operators in Hilbert Space such as compact, bounded and unbounded operators, semi-bounded operators and Friedrichs extensions, variational principle, Birman-Schwinger principle. Read more

Лекторы: Ari Laptev (Imperial College London), Lukas Schimmer (University of Copenhagen), Baibulov Ilnur (SPb State University).

Подать заявку на участие в школе можно направив письмо по адресу smc@sochisirius.ru или через форму регистрации до 15 марта 2020 года. Центр принимает заявки на оказание финансовой (проезд и проживание) поддержки, при оформлении заявок следуйте указаниям (на английском языке).

002s: Mathematics of Many-Body Quantum Systems, перенесена на 2021

Описание: The school will focus on the rigorous aspects of certain questions of high physical interest for many-body quantum systems, such as Bose-Einstein condensation in Bose gases, Cooper pairing and superconductivity in Fermi gases, screening effects in Coulomb systems. Each topic will be reviewed by a main lecturer, followed by several shorter talks on more advanced questions. A particular emphasis will be put on the derivation of effective nonlinear equations from the true many-body Schrödinger linear equation in limits where the number of particles tends to infinity. This problem has indeed generated a large amount of works in the last 10 years. The targeted audience is composed of graduate or advanced master students as well as postdocs and young researchers in Mathematical Physics and related areas.

Лекторы: Mathieu Lewin (CNRS & University of Paris-Dauphine), Robert Seiringer (IST Austria).

Подать заявку на участие в школе можно направив письмо по адресу smc@sochisirius.ru. Центр принимает заявки на оказание финансовой (проезд и проживание) поддержки, при оформлении заявок следуйте указаниям (на английском языке).

003s: Computational Bayesian Statistics in Ecology, Dec 13 - 19, 2020

Описание: Bayesian Statistics is a rich and self-contained branch of Statistics that offers both theoretical guarantees like consistency and admissibility, and practical advantages when compared with other branches. It is however often dismissed for using probability distributions on the parameters and for being associated with controversies and paradoxes. The course intends to expose the modern theory of Bayesian statistics and to demonstrate its practicality, through programming sessions with Bayesian packages and realistic applications inspired from Ecology and Genetics. A part of the course will be dedicated to so-called intractable environments when the likelihood function is well-defined but unavailable in closed form and replaced with substitutes that also guarantee convergence with the number of observations. The school is aimed at a mixed audience made both of statisticians who want to use Bayesian methods and computational tools, and biostatisticians involved in applications requiring computational statistical methods. We would like to favour the presence of younger researchers at this school. It is indeed paramount that young researchers in our research areas are exposed as early as possible to modelling and experimenting methods and analysis outside their immediate scientific surrounding. We will also seek a maximal level of interaction during and around the classes with "bring-your-own-problem" sessions. Read more.

Лекторы: Sophie Donnet (INRAE, Paris), Jean-Michel Marin (Université de Montpellier), Christian Robert (Université Paris Dauphine and University of Warwick), Julien Stoehr (Université Paris Dauphine).

Подать заявку на участие в школе можно направив письмо по адресу smc@sochisirius.ru. Центр принимает заявки на оказание финансовой (проезд и проживание) поддержки, при оформлении заявок следуйте указаниям (на английском языке).

## Завершенные мероприятия

001w: Spectral Theory and Mathematical Physics, Feb 2 - 8, 2020

Описание: The program will include invited talks that are expected to cover a wide range of topics, such as operator theory, spectral theory, scattering theory, inverse problems, periodic and ergodic operators, asymptotic methods, classical mathematical physics.

Организаторы: Alexander Fedotov (St. Petersburg State University), Nikolai Filonov (Steklov Institute, St. Petersburg), Ilya Kachkovskiy (Michigan State University), Alexander Sobolev (University College London), Tatiana Suslina (St. Petersburg State University), Dmitri Yafaev (University of Rennes 1/St. Petersburg State University), Nikita Senik (St. Petersburg State University).

Внешний сайт: http://math.nw.ru/wp/?p=2367

Программа: Program 001w

002w: Quantum Mechanics of Artificial Material Structures, Feb 16 - 22, 2020

Описание: The aim of the program is to bring together people dealing with new mathematical challenges coming from the progress in fabrication techniques allowing to construct new structures and materials. To construct and analyze models of such objects requires solving the quantum mechanical equations of motion - Schrödinger in the first place but also nonlinear Schrödinger, Dirac, and others - in situations when the configuration space has a notrivial geometry and topology. The workshop will be devoted to reviewing and discussing new developments in this area.

Организаторы: Pavel Exner (Nuclear Physics Institute of the CAS).

Внешний сайт: http://doppler.ujf.cas.cz/qmams20.html

Программа: Program 002w

003w: Integrable Systems and Automorphic Forms, Feb 23 - 29, 2020

Описание: Over the past decade has been a breakthrough in the theory of 3D dispersionless integrable systems. Based on the method of hydrodynamic reductions, extensive classification results have been obtained revealing unexpected connections with integrable conformal geometry, algebraic geometry, hypergeometric functions and modular forms. We plan to discuss these new relations during the conference.

Организаторы: Valery Gritsenko (Université de Lille/NRU HSE), Volodya Rubtsov (Université d'Angers/ITEP/IGAP, Trieste), Victor Buhshtaber (Steklov Mathematical Institute), Evgeny Ferapontov (Loughborough University).

Внешний сайт: https://ms.hse.ru/siriusfeb2020

Программа: Program 003w

## Контакты

Основной сайт центра с платформой для подачи заявок на проведение мероприятий и участие в мероприятиях находится в разработке. До его открытия и соответствующего объявления по всем вопросам можно обращаться по адресу smc@sochisirius.ru.

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