Приглашенный заслуженный профессор Университета штата Индиана в Индианаполисе, США,
Ведущий научный сотрудник кафедры

Руководитель гранта СПбГУ (Мероприятие_2 2014-2016 годы) «Развитие методов спектральной теории операторов, теории дифракции и теории интегрируемых систем».

email: aits@iupui.edu
PURE SPBU

 Directions of research

• Integrable nonlinear PDEs and related aspects of spectral theory and algebraic geometry.
• Soliton theory.
• Exactly solvable quantum field and statistical mechanics models.
• Fuchsian systems and Riemann-Hilbert problem.
• Asymptotic analysis, special functions, orthogonal polynomials,  and matrix models.
• Mathematical physics.

Basic Research papers

1. A.R. Its, V.B. Matveev, Hill’s Operators with the Finite Number of Gaps, Funcktsional Anal. i Prilozhen., 9, no. 1, (1975) 69—70.
2. A.R. Its, Asymptotics of Solutions of the Nonlinear Schr\»odinger Equation and Isomonodromic Deformations of the Systems of Linear Differential Equations, Soviet. Math. Dokl. 24, N 3, p. 452-456 (1981).
3. R.F. Bikbaev, A.I. Bobenko, A.R. Its, On Finite-Zone Integration of the Landau-Lifshitz Equation, Soviet Math. Dokl., 28, N 2, pp. 512-516 (1983).
4. A.R. Its, A.A. Kapaev, The Method of Isomonodromy Deformations and Connection Formulas for the Second Painleve Transcendent, Math. USSR Izvestiya, 31, N. 1, 193-207 (1988).
5. A.R. Its, A.G. Izergin, V.E. Korepin, N.A. Slavnov, Differential Equations for Quantum Correlation Functions, J. Mod. Phys. B, 1003, (1990); Proc. of a Conf. «Yang-Baxter Equations, Conformal Invariance and Integrability in Statistical Mechanics and Field Theory», CMA, ANU, Canberra, Australia, July 10-14, 1989, eds. M.N. Barber, P.A. Pearce, World Scientific, 1990, p. 303-338.
6. A.S. Fokas, A.R. Its and A.V. Kitaev, The Isomonodromy Approach to Matrix Models in 2D Quantum Gravity, Comm. Math. Phys. 147, 395-430 (1992).
7. A. I. Bobenko and A. R. Its, The Painlev{‘{e}} III Equation and the Iwasawa Decomposition}, Manuscripta Mathematica, 87, pp. 369-377 (1995).
8. P. A. Deift, A. R. Its, X. Zhou, A Riemann-Hilbert Approach to Asymptotic Problems Arising in the Theory of Random Matrix Models, and Also in the Theory of Integrable Statistical Mechanics, Ann. of Math. 146, 149-235 (1997).
9. P. Bleher, A. Its, Semiclassical Asymptotics of Orthogonal Polynomials, Riemann-Hilbert Problem, and Universality in the Matrix Model, Ann. of Math., 150 (1999), 185 — 266.
10. A. R. Its, The Riemann-Hilbert Problem and Integrable Systems, Notices of the AMS, Vol. 50, Number 11 (2003) 1389 — 1400
11. P. Deift, A. Its, I. Krasovsky, Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities, Annals of Mathematics, v. 174, issue 2, 2011, p. 1234-1299.

Possible research topics for students

are connected with asymptotic analysis of Toeplitz and Hankel determinants, ensembles of random matrices and correlation functions of quantum-field and spin modelts.