Alexander Aptekarev

Alexander Aptekarev - Moscow State University (RUSSIA)

Alexander Ivanovich Aptekarev earned his PhD in Theory of Functions and Functional Analysis and graduated in Physics and Mathematics from Moscow State University, Russia. Dr. Aptekarev has been Head of the Mathematics Department at the Keldysh Institute of Applied Mathematics since 2003. He has also held teaching positions in the Faculty of Mechanics and Mathematics, Department of Theory of Functions and Functional Analysis at Moscow State University, and was Head of the Laboratory of Complex Analysis and Dynamical Systems at the Russian Foundation of Mathematics. He has been a Visiting Fellow at the Center for Theoretical Physics in Marseille, and in Berlin, and a Visiting Professor at the University of Westminster, the University of Havana, and Vanderbilt University, among others. Dr. Aptekarev has participated in and co-organized more than 60 conferences and has supervised several of his students’ PhD theses. In 2007 he edited: Rational approximants of Euler constants and recurrence relations, collected papers, and in addition has published more than 30 research papers and numerous articles in reviewed journals. He has been the principal investigator in the research projects: Rational Approximants of Analytic vector functions – asymptotical theory and applications and Mathematical, numerical and experimental modelling of crystallization processes with usage of supercomputers.

RESEARCH STAY AT UC3M: MATHEMATICS DEPARTMENT

PROJECT:

The project is devoted to a fundamental problem of modeling of singularities, i.e. to create mathematical models for the processes with lost of continuity, with phase transitions or with very high frequency oscillations. We use poles of rational approximants to model singularities of analytic functions (poles, cuts between branch points). The modern applications of the expected results of the project are theory of Random matrices with various scenarios of Brownian motions and coupled matrix models of quantum gravitation.

STAY PERIOD: JAN 11 - JUL 11

Conferences

Title: "Structure of multi-valued analytic functions and rational approximants"

Author: Prof. Alexander I. Aptekarev

Date: April 6, 2011

Time: 12.30h

Place: Sala 2.2.D08

Publications

• Asymptotics of Lp-norms of Hermite polynomials and Renyi entropy of Rydberg oscillator states. A. I. Aptekarev, J. S. Dehesa, P. S´anchez-Moreno, and D. N. Tulyakov. Contemporary Mathematics, Volume 578, 2012. http://dx.doi.org/10.1090/conm/578/11469

• Rényi entropy of the infinite well potential in momentum space and Dirichlet-like trigonometric functionals. A. I. Aptekarev, J. S. Dehesa, P. Sánchez-Moreno, D. N. Tulyakov. Received: 21 October 2011 / Accepted: 30 November 2011 / Published online: 13 December 2011. © Springer Science+Business Media, LLC 2011

• Padé approximants, continued fractions, and orthogonal polynomials. A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, and S.P. Suetin. Russian Math. Surveys 66:6 1049–1131 © 2011 RAS(DoM) and LMS. Uspekhi Mat. Nauk 66:6 37–122 DOI 10.1070/RM2011v066n06ABEH004770

• Hermite–Padé approximations and multiple orthogonal polynomial ensembles. A. I. Aptekarev and A. B. J. Kuijlaars. Russian Math. Surveys 66:6 1133–1199 © 2011 RAS(DoM) and LMS. Uspekhi Mat. Nauk 66:6 123–190 DOI 10.1070/RM2011v066n06ABEH004771