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# Alexander R Its Ph.D.

Distinguished Professor, Mathematical Sciences

## Awards & Honors

### Awards

The Prize of the Moscow Mathematical Society (1976)

The Prize of the Leningrad Mathematical Society (1981)

2002 Hardy Fellow of the London Mathematical Society

2009 Batsheva de Rothschild Fellow of Israel Academy of Sciences and Humanities

### Honorable Lectureships

- Invited Address to the AMS - MAA - SIAM Joint Mathematical Meetings, January 22, 2000.
- Hardy lectures to the London (June 21.02) and to the Edinburgh (May 24.02) Mathematical Societies. Series of Hardy lectures in several universities in the UK ( March 12 - June 28, 2002 )
- Invited Speaker to the IMC 2010

## Current Research

Prof. Its' major area is integrable systems. His current research interests are concentrated in the following directions: (a) Asymptotic analysis of the matrix models and orthogonal polynomials via Riemann-Hilbert and isomonodromy methods; (b) The asymptotic analysis of the correlation functions of quantum exactly solvable models and the related aspects of the theory of Fredholm and Toeplitz operators; (c) The theory of integrable nonlinear partial and ordinary differential equations of the KdV and Painleve types.

In the area of random matrices, Its' main results for the last seven years have been obtained in collaboration with Pavel Bleher, as described above.

The asymptotics of correlation functions has been a major theme of Its' research for the last 20 years. The most recent of Its' efforts in the area of correlation functions are concerned with the problem of evaluation of quantum entanglement in the XY spin chain. The problem has been attracting a great deal of interest because of its relevance to quantum information processing. Using the Riemann-Hilbert approach, Its, together with V. Korepin and B.-Q. Jin (SUNY at Stony Brook), has evaluated the principal characteristic of the entanglement-the limiting entropy of a block of spins.

In the area of integrable equations, Its is pursuing several long-term projects addressing the global analytic properties of the solutions of integrable equations. One of the most recent of Its' efforts in this area is represented by a series of papers on the Riemann-Hilbert approach to the initial-boundary value problems for nonlinear Schroedinger equation.

## Select Publications

A. R. Its, F. Mezzadri, and M. Y. Mo, Entanglement entropy in quantum spin chains with finite range interaction, Communications in Mathematical Physics, vol: 284 (2008), 117-18.

A. Its, I. Krasovsky, Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump, Contemporary Mathematics, v. 458 (2008), 215-247.

A. R. Its, A. B. J. Kuijlaars and J. Ostensson, Critical Edge Behavior in Unitary Random Matrix Ensembles and the Thirty-Fourth Painleve Transcendent, IMRN, Volume 2008: article ID rnn017, (2008) 67 pages.

T. Claeys, A. Its, and I. Krasovsky, Higher order analogues of the Tracy-Widom distribution and the Painleve II hierarchy, to appear in Comm. Pure. Appl. Math. (arxiv:0901.2473)

P. Deift, A. Its, and I. Krasovsky, Asymptotics of Toeplitz, Hankel, and Toeplitz + Hankel determinants with Fisher-Hartwig singularities, preprint, arXiv: 0905.0443

A.R. Its, Asymptotics of Solutions of the Nonlinear Schrodinger Equation and Isomonodromic Deformations of the Systems of Linear Differential Equations, Soviet. Math. Dokl. 24, N 3, p. 452-456 (1981).

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).

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).

P. Bleher, A. Its, Double Scaling Limit in the Random Matrix Model: the Riemann-Hilbert Approach, Communications in Pure and Applied Mathematics, Vol. LVI, (2003) 433 - 516.

P. Deift, A. Its, I. Krasovsky, Asymptotics of the Airy-kernel determinant, Communications in Mathematical Physics 278, 3 643-678 (2008).

- phone: (317) 278-1081
- office: LD 224L
- e-mail: aits@iupui.edu

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