CHEKHOV Leonid Olegovitch

Vita and Education:

Born: March, 29 1962 (Moscow)

Student of Physical Department of Moscow State University, 1978-1984;

Postgraduate student in Steklov Mathematical Inst., Moscow, 1984-1987;

Ph.D. (Candidate of Physical and Mathematical Sciences) in Steklov Math. Inst., Moscow in 1987. Doctorial Dissertation in Steklov Math. Inst. in 2001.

Title of thesis: "Matrix models and geometry"

Has two children aged 13 and 20.

Permanent place of employment:

Department of Theoretical Physics, Steklov Mathematical Institute


Courses in theoretical mechanics, field theory, and string theory in the College of Mathematical Physics of Independent Moscow University in years 1994--2001. Courses in calculus and in complex variable function theory in Moscow Physico-Technical Institute 2003-2004.

Area of specialization:

Quantum field theory: gauge and supersymmtric theories, matrix models and integrable systems, graph theory.

Recent visiting positions

Visiting scientist in ICTP, Trieste 1989, 2003, in Enrico Fermi Inst., Chicago, 1991, in NORDITA, February 1993; stagier in 1992-1993 in Laboratoire de Physique Theorique et Hautes Energies, Universite Paris-VI-VII, visiting professor in Niels Bohr Inst., 1993, 1995, 97, 98, 99, 00, 01; in Ecole Polytechnique, Paris 1996, in Univ. of Southern California, 2003 and other.

Recent invited talks

Stony Brook 01, Copenhagen 01, Utrecht 02, Kiev 03, Prague 04, Potsdam 04, at String Program at Fields Inst., 04-05, etc.

Summary of current research:

In matrix models we investigate the newly appeared fascinating topic: the so-called multicut solutions to standard matrix models. These solutions have found a lot of applications in geometry of integrable systems and in description of vacua of N=2 supersymmetric gauge (Yang--Mills) theories with the supersymmetry broken to N=1 since 2001. In earlier papers, [6] and [7], we have proved that these solutions possess the WDVV equations in the leading term of 't Hooft topological expansion and in [4] the next-to-leading term (the so-called torus correction) was found. we review these and some other new geometrical results in [1].

In [3], a new concept of quantum Thurston theory was proposed and its self-consistency was proved. We associate quantum operators to the points of the closure of the space of observables of 2D theory. Those observables [8] are associated with closed geodesics on the Riemann surface, while taking the closure corresponds to considering geodesics of infinite length, which are objects of studying in the classical Thurston (train track) theory. We prove that using the quantization procedure by Chekhov and Fock [10] based on the graph description by Penner and Fock of the Teichmuller spaces, we can construct operators that admit a continuous limit when going to the closure of the observable space.

In [2], the 2-point correlation functions of the CFT on torus were proved to be in the correspondence to the AdS gravity correlation functions in the 3D filling of this torus if we take all possible filling (enumerated by coprime positive integers (m,n)).

Recent papers

1) Matrix models: Scrapbook of recent results By L. Chekhov, A. Marshakov, A. Mironov, and D. Vassiliev, in preparation, to be published in Proc. Steklov Math. Inst.

2) AdS$_3$/CFT$_2$ on torus in the sum over geometries. By L.Chekhov hep-th/0409113, to appear in Proc. of Intl. Conf. Quarks'04.

3) On quantizing Teichmuller and Thurston theories. By L. Chekhov and R.C. Penner e-Print Archive:; subm. to Commun.Math.Phys.

4) Introduction to quantum Thurston theory. By L.O.Chekhov and R.C.Penner Russ.Math.Surv. 58(6):1141-1183,2003.

5) Genus one correction to multicut matrix model solutions. By L. Chekhov e-Print Archive: hep-th/0401089; subm. to Theor.Math.Phys.

6) DV and WDVV. By L. Chekhov, A. Marshakov, A. Mironov, and D. Vasiliev Phys.Lett.B562:323-338,2003; e-Print Archive: hep-th/0301071

7) Matrix models versus Seiberg-Witten / Whitham theories. By L. Chekhov and A. Mironov Phys.Lett.B552:293-302,2003; e-Print Archive: hep-th/0209085

8) Observables in 2+1 gravity and noncommutative Teichmueller spaces. By L.O. Chekhov Theor.Math.Phys.129:1609-1616,2001.

9) Matrix models: geometry of moduli spaces and exact solutions. By L.O. Chekhov Theor.Math.Phys.127:557-618,2001.

10) Observables in 3d gravity and geodesic algebras. By L.O. Chekhov and V.V. Fock Czech.J.Phys.50:1201-1208,2000