# GEOMETRY, GROUPS, OPERATOR ALGEBRAS, AND INTEGRABILITY 2022

## International conference

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This conference is focused on three closely related subjects: groups and their actions in geometry and topology, operator algebras, and integrable systems. These branches of mathematics are important in themselves and have wide applications in various areas. Geometric ideas and methods play a crucial role in interconnection and development of these fields. Integrability and other properties of dynamical systems are often related with geometry and symmetries of these systems, i.e., group actions. Many operator algebras are produced from groups and bear group action, so that properties of these algebras reflect properties of the corresponding groups and vice versa. Quantum mechanics and modern physical theories use operator algebras as a basic tool. There are many other similar examples of mutual interference of these fields.

The main purpose of the conference is to bring together experts in the major fields listed in its title. We hope that this will help disseminating important ideas and broaden the areas of mutual interest.

The main topics of the conference are:

 Lie, holomorphic, and algebraic transformation groups
 Discrete subgroups of Lie groups and discrete transformation groups
 Quantum groups and universal enveloping algebras
 Representation theory
 Geometry and topology of manifolds
 Equivariant topology
 Elliptic operators on manifolds and index theory
 Operator algebras and K-theory of C*-algebras
 Geometry of integrable systems
 Algebraic methods of integration
 Integrable models in physics
 Higher structures in physics and geometry

#### Organizers

Sergey Dobrokhotov, Huijun Fan, Anatoly Fomenko, Elena Kudryavtseva, Vladimir Manuilov, Dmitry Millionshchikov, Eva Miranda, Andrey Mironov, Alexander Mishchenko, Vladimir Nazaikinskii, Andrey Oshemkov, Vladimir Podolskiy, Fedor Popelensky, Tudor Ratiu, Anton Savin, Armen Sergeev, Andrei Shafarevich, Georgy Sharygin, Dmitry Timashev, Alexander Zheglov, Nguyen Tien Zung

### INVITED SPEAKERS

The final list of keynote speakers includes:

•   Anton Alekseev, Université de Genève
•   Andrey Domrin, Lomonosov Moscow State University
•   Evgeny Ferapontov, Loughborough University
•   Vladimir Fock, Université de Strasbourg
•   Petr Grinevich, Steklov Mathematical Institute, Moscow
•   Valery Gritsenko, Université de Lille, HSE University, Moscow
•   Sabir Gusein-Zade, Lomonosov Moscow State University
•   Sergei Ivanov, St. Petersburg Department of Steklov Mathematical Institute
•   Yuri Kordyukov, Institute of Mathematics, Ufa Federal Research Centre
•   Andrey Mikhovich, Moscow Center for Fundamental and Applied Mathematics
•   Dmitry Millionshchikov, Lomonosov Moscow State University
•   Eva Miranda, Universitat Politècnica de Catalunya – BarcelonaTech
•   Aleksandr Mishchenko, Lomonosov Moscow State University
•   Alexander Molev, University of Sydney
•   Vladimir Nazaikinskii, Ishlinsky Institute for Problems in Mechanics, Moscow
•   Nikita Nekrasov, Stony Brook University
•   Victor Nistor, Institut Élie Cartan de Lorraine, Nancy
•   Taras Panov, Lomonosov Moscow State University
•   Yongbin Ruan, Zhejiang University
•   Georgy Sharygin, Lomonosov Moscow State University
•   Fedor Sukochev, University of New South Wales, Kensington
•   Iskander Taimanov, Sobolev Institute of Mathematics, Novosibirsk
•   Weiping Zhang, Nankai University, Tianjin

### Participants

List of registered participants:

Petr Akhmet'ev(IZMIRAN)
Oleg Aristov(Moscow)
Dmitry Artamonov(Lomonosov MSU)
Andronick Arutyunov(V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences)
Varuzhan Atabekyan(Yerevan State University)
Amine Bahayou(Kasdi Merbah University)
Ilnur Baibulov(SPbU, Euler Mathematical Center)
Dogukan Bakircioglu(Sorbonne University)
Panagiotis Batakidis(Aristotle University Thessaloniki)
Sandipan Bhattacherjee(Birla Institute of Technology Mesra, Ranchi, India)
Xavier Blot(Weizmann Institute)
Neda Bokan(University of Belgrade - Faculty of Mathematics)
Egor Bushuev(Prokhorov General Physics Institute of RAS, Moscow)
Mikhail Chernavskikh(MSU)
Nikhilesh Dasgupta(National Research University Higher School of Economics)
Tobias Diez(SJTU)
Andrei Ershov(MIPT)
Matthias Franz(University of Western Ontario)
Olga Frolkina(M.V.Lomonosov Moscow State University)
Denis Fufaev(Moscow Center of Fundamental and Applied Mathematics, Lomonosov MSU)
Daciberg Goncalves(Institute of Mathematics and Statistic - University of São Paulo)
Laura Gonzalez Bravo(Universidad Carlos III de Madrid)
Andrew Gorbach(Moscow)
Vladislav Grauman(Moscow State University)
Evgeniy Gudkov(Russian Youth Polytechnic Society)
Dmitry Gugnin(Lomonosov Moscow State University)
Yasushi Ikeda(Lomonosov Moscow State University)
Anwar Irmatov(Lomonosov Moscow State University )
Petr Ivankov(MSU)
Vladislav Kibkalo(Lomonosov MSU, Moscow Center for Fundamental and Applied Mathematics)
Nuriddin Komilov(Andijan State University)
Roman Kozlov(Sobolev institute of mathematics)
J. Kukke Prasanna(Bengaluru City University)
Andrey Lazarev(Lancaster University, UK)
Yan Li(Beijing Institute of Technology, School of Mathematics and Statistics)
Jalolxon Nuritdinov(National University of Uzbekistan)
Jose Oliveira(University of Minho)
Rukhsat Parmanova(Institute of Nuclear Physics of Academy of Science of Republik of Uzbekistan)
Milan Pavlovic(Faculty of Mathematics, University of Belgrade, Serbia)
Alexander Perepechko(IITP RAS; HSE)
Milos Petrovic(University of Nis, Serbia)
Claudiu C. Remsing(Rhodes University, Grahamstown, South Africa)
Miguel Angel Rosas Villalobos(Universidad del Bio-Bio)
Khalid Saifullah (Quaid-i-Azam University, Islamabad )
Karuppaiya Sakkaravarthi(Asia Pacific Center for Theoretical Physics (APCTP), South Korea)
Anton Savin(RUDN University)
Xurshid Sharipov(Samarkand State University)
Kumar Sannidhya Shukla(University of Western Ontario, Canada.)
Alexey Silantyev(Joint Institute for Nuclear Research, State University "Dubna")
Dmitry Sinelshchikov(HSE University)
Mikhail Skopenkov(HSE University and IITP RAS)
Roman Stasenko(Lomonosov Moscow States University)
Vladimir Stukopin(Moscow Institute of Physics and Technology)
Oleg Styrt(MSU, MIPT)
Dmitry Talalaev(Moscow State University)
Sa'dulla Tashpulatov(Institute of Nuclear Physics of Academy of Sciences of Republik of Uzbekistan)
Vladimir Vershinin(Universite de Montpellier, Montpellier, France)
Emanuel Viana(Instituto Federal de Educação, Ciência e Tecnologia do Ceará - IFCE)
Elizaveta Vishnyakova(Universidade Federal de Minas Gerais)
Dmitriy Zanin(University of New South Wales, Kensington)

### PROGRAM

of the conference

The final conference schedule is given in the table below. The talk titles are clickable and linked to video records or slides of talks. The PDF file of the book of abstracts can be downloaded here.

Day Time Speaker Title Location
Monday
June 27, 2022
0900 - 0950 Registration Hall
0950 - 1000 Opening B5
1000 - 1050 Sabir Gusein-Zade Mirror symmetry on invariants of the Berglund-Hübsch-Henningson-dual non-commutative orbifolds and its distribution among levels Plenary: B5
1050 - 1120 Coffee break Hall
1120 - 1210 Taras Panov Holomorphic foliations on complex moment-angle manifolds Plenary: B5
1220 - 1310 Eva Miranda Looking at Poisson manifolds through new symplectic glasses Plenary: B5
1320 - 1500 Lunch
1500 - 1550 Dmitry Millionshchikov Einstein derivations and narrow Lie algebras Plenary: B5
1600 - 1640 Anton Savin A local index formula for the spectral triple associated with metaplectic operators Section 1: B2
Alexander Perepechko Automorphism groups consisting of algebraic elements Section 2: B5
1640 - 1710 Coffee break Hall
1710 - 1750 Denis Fufaev Counterexamples in Hilbert $$C^*$$-modules theory Section 1: B2
Roman Stasenko Short $$SL_2$$-structures on simple Lie algebras Section 2: B5
1800 - 1840 Oleg Aristov Banach algebras of polynomial growth and universal algebras of non-commutative $$C^\infty$$-functions Section 1: B2
Vladislav Kibkalo Degenerate singularities of mechanical systems Section 2: B5
Tuesday
June 28, 2022
1000 - 1050 Vladimir Nazaikinskii Uniformization, symplectic reduction, and asymptotic solutions Plenary: B5
1050 - 1120 Coffee break Hall
1120 - 1210 Weiping Zhang Deformations of Dirac operators and applications Plenary: B5
1220 - 1310 Yuri Kordyukov Semiclassical trace formulas for the Bochner Laplacian on a Hermitian line bundle Plenary: B5
1320 - 1500 Lunch
1500 - 1550 Iskander Taimanov Closed geodesics on non-simply-connected manifolds Plenary: B5
1600 - 1640 Vladimir Stukopin Super Yangians and quantum loop superalgebras Section 1: B2
Petr Akhmet'ev Classifying space for double points of skew-framed immersions Section 2: B5
1640 - 1710 Coffee break Hall
1710 - 1750 Alexey Silantyev Quantum Representation Theory and Manin matrices Section 1: B2
Andrey Lazarev Higher local systems, loop spaces, and derived categories of second kind Section 2: B5
1800 - 1840 Roman Kozlov Standard bases method for vertex algebras Section 1: B2
Dmitry Gugnin Any suspension and any homology sphere are 2H-spaces Section 2: B5
Wednesday
June 29, 2022
1000 - 1050 Fedor Sukochev Quantum differentiation and integration for the quantum plane Plenary: B5
1050 - 1120 Coffee break Hall
1120 - 1210 Georgy Sharygin Quantising the argument shift method: quasi-derivations and other constructions Plenary: B5
1220 - 1310 Vladimir Fock Cluster duality and Satake correspondence Plenary: B5
1320 - 1500 Lunch
1500 - 1550 Anton Alekseev Poisson brackets and flat connections Plenary: B5
1800 -          Conference dinner Restaurant Chuanyui
Thursday
June 30, 2022
1000 - 1050 Yongbin Ruan Logarithmic R-map Plenary: B5
1050 - 1120 Coffee break Hall
1120 - 1210 Valery Gritsenko Chevalley type theorem for Jacobi modular forms and non-linear differential equations Plenary: B5
1220 - 1310 Aleksandr Mishchenko Comparison of Hochschild homology and cohomology of group algebras Plenary: B5
1320 - 1500 Lunch
1500 - 1550 Evgeny Ferapontov Dispersionless integrable equations and modular forms Plenary: B5
1600 - 1640 Vladimir Vershinin On homotopy braids Section 1: B2
Dmitry Talalaev Electrical networks and positive lagrangian grassmanian Section 2: B5
Neda Bokan Geometry of cotangent bundle of Heisenberg group Section 3: B3
1640 - 1710 Coffee break
1710 - 1750 Daciberg Goncalves Free actions of discrete groups on even dimension homotopy spheres Section 1: B2
Dmitry Sinelshchikov Integrability criteria for autonomous and non-autonomous second-order differential equations Section 2: B5
Emanuel Viana Critical metrics on 4-manifolds with harmonic anti-self dual Weyl tensor Section 3: B3
1800 - 1840 Matthias Franz The cohomology rings of homogeneous spaces Section 1: B2
Oleg Styrt On matrix sets with special properties Section 2: B5
Friday
July 01, 2022
1000 - 1050 Alexander Molev Affine center at the critical level and quantum Mishchenko-Fomenko subalgebras Plenary: B5
1050 - 1120 Coffee break Hall
1120 - 1210 Victor Nistor On the index of G-invariant pseudodifferential operators Plenary: B5
1220 - 1310 Andrey Domrin Holomorphic solutions of integrable evolution equations Plenary: B5
1320 - 1500 Lunch
1500 - 1550 Andrey Mikhovich Arithmetic squares and demystification of J.-P. Serre's philosophy Plenary: B5
1600 - 1640 Andrei Ershov On a generalization of the topological Brauer group Section 1: B2
Andronick Arutyunov Derivations on bimodules Section 3: B3
1640 - 1710 Coffee break Hall
1710 - 1750 Olga Frolkina An answer to a question of J.W. Cannon and S.G. Wayment Section 1: B2
Elizaveta Vishnyakova Donagi-Witten construction and a graded covering of a supermanifold Section 2: B5
Jose Oliveira On the sheaf of smooth forms on Lie algebroids over triangulated spaces Section 3: B3
1800 - 1840 Mikhail Skopenkov Feynman checkers: Minkowskian lattice quantum field theory Section 2: B5
Panagiotis Batakidis Courant algebroids and representations Section 3: B3
Saturday
July 02, 2022
1130 - 1210 Karuppaiya Sakkaravarthi Similarity transformation to explore variable-coefficient nonlinear model equations: dynamics of solitons, breathers, and rogue waves in inhomogeneous media Section 1: zoom
Dmitriy Zanin $$C^{\ast}$$-algebraic approach to the principal symbol Section 2: zoom
1220 - 1300 Khalid Saifullah The Johannsen-Psaltis spacetime with charge Section 1: zoom
Anwar Irmatov Asymptotic enumerations of threshold functions and singular $$\pm1$$-matrices Section 2: zoom
1310 - 1350 Petr Ivankov Noncommutative coverings and prospects of their applications to the theoretical physics Section 1: zoom
1400 - 1600 Lunch
1600 - 1650 Sergei Ivanov Recent progress in ellipsoid characterization problems Plenary: zoom
1700 - 1750 Petr Grinevich Double-periodic rogue waves type solutions of the focusing Davey-Stewardson-2 equation: the finite-gap approach Plenary: zoom
1810 - 1900 Nikita Nekrasov Many faces of Calogero-Moser system as seen by sigma models and gauge theories Plenary: zoom

### Financial Support

of the conference

The conference is supported by the Moscow Center of Fundamental and Applied Mathematics.

The organizers provide free accommodation for participants at the dormitory of Moscow State University. Due to limited funds, we can support only a very small number of participants. So we recommend that applicants who need financial support look for travel grants at home or consider online participation.

If you need financial support for your participation in GGOI 2022, please indicate this in the registration form.

### Venue

of the conference

The conference takes place in the Shuvalov Building of Lomonosov Moscow State University, ground floor.

### CONTACT

Leninskie Gory 1, Moscow, 119991, Russia

ggoi2022@mathcenter.ru