In the framework of a visit of a delegation of the Shanghai Transportation University (Shanghai Jiao Tong University) to the MSU, the representatives of the School of Mathematics of the Shanghai Transportation University Professors Zhen Zhao and Dongmei Xiao visited Bogolyuubov Laboratory of Geometrical Methods in Mathematical Physics on 03.09.2018. At the Laboratory Seminar the researchers of Laboratory delivered scientific talks: N.Yu.Erokhovetz "Geometry and Topology of fullerenes" and M.V.Pavlov "Classical mechanical systems with one one-and-a-half degrees of freedom". The presentation by Professor Dongmei Xiao was devoted to the history of the Shanghai Transportation University, its celebrated alumni and the current research in mathematics and mechanics in the STU.

N.Yu.Erokhovetz	Participants	Audience

M.V.Pavlov	Dongmei Xiao

An agreement between the MSU and the Shanghai Transportation University about cooperation in the field of mathemetics between laboratories was signed on 04.09.2018. The MSU is represented by the Bogolyubov Laboratory of Geometrical Methods in Mathematical Physics and the Shanghai Transportation University is represented by the Center of Mathematical Sciences named after Wu Wenjun.

Infinite-dimensional integrable systems of Mathematical Physics

Soliton_hydro.jpg from Wikipedia

(B.Dubrovin, M.Pavlov, A.Mironov, P.Grinevich and others)

One of the main directions of research in the Laboratory is the study of integrable systems of the hydrodynamic type. In 1984 B.Dubrovin and S.Novikov have constructed a Hamiltonian formalism for Whitham systems. It turned that the Poisson brackets of this type are generated by flat pseudo-Riemannian metrics on manifolds, where the considered fields take values. This metric is not constant in the naturally arising coordinates and a reduction of the bracket to canonical form is a very non-trivial problem. The approach to the integration of these systems (generalized hodograph method) ... Read more in Russian »

Low-dimensional topology

(I.Dynnikov, L.Alania, A.Skripchenko and others)

In the framework of this direction we study combinatorial properties of rectangular diagrams of links, of braid groups and mapping class groups, periodic surfaces in the 3-space and R-trees.

In 2004 I.Dynnikov has proved that all rectangular diagrams of the trivial knot admit a monotone reduction to the trivial diagram... Read more in Russian »

Non-commutative geometry and mathematical physics

Calabi-Yau.png from Wikipedia

(V.Manuilov, E.Troitsky, A.Mishchenko, D.Millionshchikov, A.Penskoi and others)

The analogy between the quantization and the passage from commutative to non-commutative geometry lies in the basement of applications of non-commutative geometry methods in mathematical physics. The essence of this analogy is as follows. Consider a "good" topological space X. It corresponds to a C*-algebra... Read more in Russian »

Combinatorial topology, polyhedra

(V.Buchshtaber, T.Panov, A.Gaifullin and others)

The general theory of toric actions has a long history of development and forms an important field in the domain of equivariant topology. Simultaneously with this development a new domain, named toric topology, arised. The toric topology studies algebraic, combinatorial, differential and homotopy aspects of torus actions with a rich combinatorial structure of their orbit spaces. An important property of this field is ... Read more in Russian »

Computer and computational methods

(C.Klein, P.Grinevich, R.Razumovskiy and others)

Several rather independent computational approaches are developed in the Laboratory. These directions can be splitted in three groups, closely related with the basic theoretical problems of our research groups. Read more in Russian »

• Buryak, A.; Shadrin, S. A new proof of Faber's intersection number conjecture. Advances in Mathematics. 228 (2011), no. 1, 22-42.
• Carlet Guido; Dubrovin Boris; Mertens Luca Philippe. Infinite-dimensional Frobenius manifolds for 2+1 integrable systems. Mathematische Annalen 349 (2011) , Issue: 1, 75-115.
• Manuilov Vladimir; Thomsen Klaus. Semi-invertible extensions of C*-algebras. Journal of Functional Analysis. 260 (2011), Issue: 5, 1446-1462.
• Grinevich P.G., Novikov R.G. Faddeev eigenfunctions for point potentials in two dimensions. Physics Letters A, 376 (2012), 1102-1106.
• Grinevich P.G., Novikov R.G. Moutard transform for the generalized analytic functions. Journal of Geometric Analysis. 26 (2016), 2984-2995.
• Grinevich P.G., Santini P.M. Nonlocality and the inverse scattering transform for the Pavlov equation. Studies in Applied Mathematics. 137 (2016), 10-27.
• Boris Dubrovin, Si-Qi Liu, Di Yang, Youjin Zhang. Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs. Adv. Math. 293 (2016) 382-435.
• B.Dubrovin, T.Grava, C.Klein. On critical behaviour in generalised Kadomtsev - Petviashvili equations. Physica D 333 (2016) 157-170.
• B.Dubrovin, M.Bertola, Di Yang Correlation functions of the KdV hierarchy and applications to intersection numbers over M_g,n. Physica D 327 (2016) 30-57.
• Boris Dubrovin, Di Yang. Generating series for GUE correlators. Letters in Mathematical Physics 107 (2017) 1971-2012.
• Boris Dubrovin, Si-Qi Liu, Youjin Zhang. Bihamiltonian Cohomologies and Integrable Hierarchies II: The Tau Structures. Communications in Mathematical Physics. Published Online 14 June 2018.

More publication in Russian pages »

• Boris Dubrovin
• Ivan Dynnikov
• Piotr Grinevich
• Vladimir Manuilov
• Dmitri Millionshchikov
• Andrey Mironov
• Roman Novikov
• Maxim Pavlov
• Alexei Penskoi
• Vladimir Shastin
• Evgenij Troitsky

More our researchers in Russian pages »

Some persons in international cooperation with the Lab

• Francesco Calogero (University of Rome La Sapienza, Italy)
• George Bluman (University of British Columbia, Canada)
• Mark Mineev-Weinstein (Los Alamos Laboratory, USA)
• Alexander Veselov (Loughborough University, UK)
• Igor Krichever (Columbia University, USA)
• Anatoly Neishtadt (Loughborough University, UK)
• Christian Klein (Université de Bourgogne, Dijon, France)
• Valentin Ovsienko (Reims, France)
• Paolo Maria Santini (Department of Physics, University of Roma "La Sapienza", Italy)
• Roberto De Leo (Howard University, Washington, USA)
• Jozef H. Przytycki (George Washington University, Washington, USA)
• Youjin Zhang (Tsinghua University, Beijing, China)
• Si-Qi Liu (Tsinghua University, Beijing, China)y
• John Millson (University of Maryland, USA)
• Guido Carlet (Université de Bourgogne, Dijon, France)

More about our international cooperation in Russian pages »

• International Conference "Geometric Structures in Integrable Systems" (October-November 2011)
• International Conference "Algebraic Structures in Mathematical Physics" (December 2012)
• International Conference "Geometry, Topology, Integrable Systems" (June 2013)
• International Conference "Turbulence and wave processes" (November 2013)
• International School "Geometrical Methods in Mathematical Physics" 2011
• International School "Geometrical Methods in Mathematical Physics" 2012
• International School "Geometrical Methods in Mathematical Physics" 2013
• International School "Geometrical Methods in Mathematical Physics" 2014
• International School "Geometrical Methods in Mathematical Physics" 2015
• International School "Geometrical Methods in Mathematical Physics" 2016

More our conferences, schools and other activities in Russian pages »