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Chebyshyov Interdisciplinary Research Laboratory

Contract number
11.G34.31.0026
Time span of the project
2010-2014

As of 18.05.2020

48
Number of staff members
447
scientific publications
General information
Name of the project:  Probability and analysis in the modern mathematical physics


Strategy for Scientific and Technological Development Priority Level: a



Goals and objectives

Project objective: Investigating various topics on the junction of mathematical analysis, probability theory, mathematical and theoretical physics

Research directions: Mathematics


The practical value of the study

  • Critical behavior of the 2D Ising model has been studied.
  • We have proven the Nadirashvili’s conjecture on the measure of nodal sets of eigenvalues of the Laplace–Beltrami operator.
  • We have studied relations between harmonic functions and the global nodal set, in case the dimensionality of 3 for such functions we have proven Harnack's inequality.
  • Our researchers have developed the theory of presheaves with framed transfers and presented an explicit construct for the stable motivic homotopy category.
  • We have solved the motivic analog of the Serre theorem on the number of homologous groups.
  • Our researchers have solved the Bousfeld problem for finitely presented metabelian groups and for finitely generated free groups.
  • Relation between the Rost invariant and shells of twisted flag varieties has been described.
  • We have investigated the problem of spectral synthesis for a number of functional spaces.
  • The Bellman function method in harmonic analysis has been developed.
  • New results have been obtained in enumerative combinatorics of maps, hypermaps, meanders and other objects of geometric nature.

Education and career development:

  • 3 doctoral dissertations and 26 candidate dissertations have been defended.
  • We have organized internships at the Laboratory for 115 young mathematicians (students, postgraduates and young researchers).
  • The Laboratory has conducted over 2070 educational and scientific seminars. Seminars in mathematical analysis, K-theory and the theory of motives (a field of mathematics on the boundary of algebraic geometry and homological algebra), algebraic groups theory, numbers theory and combinatorics are regularly held at the Laboratory.
  • Our researchers have read over 200 lecture courses and mini-courses. Among the lecturers were both members of the academic staff of the Laboratory and renowned Russian and foreign researchers: Gerhard Huisken (director of the Mathematical Research Institute of Oberwolfach), Harald Helfgott (senior researchers at CNRS), Jean-Louis Colliot-Thelene (professor at Paris · University), Martin Hairer (professor at Imperial College London, Fields Medalist), Rpstoslav Grigorchuk (professor at Texas A&M University), Louis de Branges (professor at Purdue University), Dmitriy Orlov (corresponding member of the Russian Academy of Sciences), Alexandr Kuznetsov (corresponding member of the Russian Academy of Sciences) and others.
  • We have supported organization of over 65 conferences and summer schools. Among them are «St. Petersburg School in Probability and Statistical Physics» in 2012 with participation of over 200 people; the series of conferences in algebra and algebraic geometry (Workshop «Reductive groups and related structures», International Arithmetic Conference dedicated to the 70th birthday of S.V. Vostokov, «Algebraic geometry and applications to physics and dynamics», «Arithmetic geometry, Chow groups and rational points») in 2015; a one-semester thematic program in complexity theory that featured 3 workshops and a series of lecture courses.

Organizational and structural changes:

  • In 2015 with support from the Chebyshyov Interdisciplinary Research Laboratory, the Saint Petersburg state University launched the bachelors degree program in mathematics. Tutoring is conducted within the new educational program «Mathematics» (01.03.01) aimed at preparing multi-skilled professionals in the fields of mathematics and theoretical informatics.
  • In 2018 with support from the Laboratory and the «JetBrains» company the Saint Petersburg State University has launched the «Modern programming» bachelor degree program.
  • In 2019 the «Modern mathematics» master degree program was launched with support from the P. L. Chebyshev Laboratory as well as the «Mathematics, Algorithms and Data analysis» bachelor degree program in collaboration with Yandex.

Other results:

In collaboration with the Government of the Russian Federation we have been implementing the «Lamé Department» – a competition for the invited professor chair at the Laboratory. The winner will be selected from mathematicians working at state foundations of France. Preference is given to candidates whose activities combine depth of theoretic research and attention to its applications. The winner of the competition will spend three months at the Saint Petersburg State University, during which the winner will read a course of lectures and conduct a seminar and a conference in their research domain. The competition has been conducted since 2014, 8 invited professors have spent three months each at the Laboratory: Alexandr Zvonkin (professor at the University of Bordeaux), Frédéric Klopp (professor at Pierre and Marie Curie University – Paris 6), Harald Helfgott (senior researcher at CNRS, head of the Adams and the Whitehead prizes), Jean-Louis Colliot-Thélène (professor at Paris-Sud University, FIelds medalist, recipient of Grand Prix of the French Academy of Sciences), Alexandr Bufetov (snior researcher at the Institute of Mathematics, University Aix-Marseille), Zhan Shi (professor at Pierre and Marie Curie University – Paris 6), Andrzej Zuk (professor at Paris Diderot University – Paris 7), Athanase Papadopoulos (University of Strasbourg).

Collaborations:

  • Saint Petersburg Branch of the Steklov Mathematical Institute of the Russian Academy of Sciences (Russia): joint seminars, joint organization of conferences, joint scientific research in mathematical and functional analysis, K-theory, partial differential equations, collaborative publications, joint organization of seminars and conferences (the annual Saint Petersburg conference in mathematical analysis, the annual conference «Diffraction days», the annual conference in spectral theory and others)
  • Higher School of Economics (Russia): joint research in the field of enumerative geometry, joint publications, organization of conferences (in particular the «Algebraic Geometry and its Applications» conference with participation of such outstanding mathematicians as Phillip Griffiths, John Morgan, Daniel Huybrechts, Claire Voisin and others)
  • «Gazprom neft» PJSC (Russia): joint research in new mathematical models related to extraction of petroleum
  • Steklov Mathematical Institute of the Russian Academy of Sciences (Russia): joint research in fundamental mathematics, joint seminars, collaborative publications
  • Université de Genève (Switzerland), Universite Bordeaux (France), University of Rennes 1 (France), University of Lille (France), Universite Aix-Marseille (France), TIFR (India), Michigan State University (USA), Royal Instiute of Technology (Sweden), Duisburg-Essen University (Germany), Universitat Osnabrueck (Germany), University of Munich (Germany), Concordia University (Canada), Norwegian University of Science and Technology Trondheim (Norway): joint research in many areas of fundamental mathematics and its applications, collaborative publications


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Logunov A.
Nodal sets of Laplace Eigenfunctions: Proof of Nadirashvili’s Conjecture and of the Lower Bound in Yau’s Conjecture. Annals of Mathematics 187(1): 241–262 (2018).
Logunov A.
Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure. Annals of Mathematics 187(1): 221–239 (2018).
Manukyan L., Montandon S.A., Fofonjka A., Smirnov S., Milinkovitch M.C.
A Living Mesoscopic Cellular Automaton Made of Skin Scales. Nature 544(7649): 173–179 (2017).
Baumslag G., Mikhailov R., Orr K.
Localization, Metabelian Groups and Isomorphism Problem. Transactions of the American Mathematical Society 369(10): 6823–6852 (2017).
Chelkak D., Smirnov D.
Universality in the 2D Ising Model and Conformal Invariance of Fermionic Observables. Inventiones Mathematicae 189(3): 515–580 (2012).
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