B.S. and M.A. in Mathematics (1986), Havana University, Cuba
Ph. D. in Mathematics (1991) State Moscow University "M.V. Lomonosov", Russia
Before joining Baylor University, Dr. Martinez-Finkelshtein was full professor of applied mathematics at the University of Almeria, Spain (1994-2017). Andrei will start teaching full time at Baylor in January 2018, keeping an affiliation with Almeria. He also taught at the Havana University, Cuba (1991-1994) and held visiting positions at several universities in Spain (Universidad Autonoma de Madrid, and Universidad Carlos III de Madrid) and the United States (University of South Florida and Vanderbilt University). He is member of several professional societies, and currently, vice-chair of the SIAM Activity Group "Orthogonal Polynomials and Special Functions". He is also in the editorial board of four journals. He loves gadgets, and his hobbies include listening to music, reading, swimming, and meeting friends.
Academic Interests and Research
Dr. Martinez-Finkelshtein's research areas include approximation theory, orthogonal polynomials, special functions and applications, Riemann-Hilbert problems and asymptotic analysis, complex and numerical analysis, and mathematical modelling, in particular, in ophthalmology and vision science.
Recent Selected Publications
A. Martínez-Finkelshtein, G. Silva, Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight
, Advances in Mathematics 349 (2019), 246-315.
A. Martínez-Finkelshtein, Brian Simanek, Barry Simon, Poncelet's Theorem, Paraorthogonal Polynomials and the Numerical Range of Compressed Multiplication Operators
, Advances in Mathematics 349 (2019), 992-1035.
A. Martinez-Finkelshtein, E. A. Rakhmanov, Do orthogonal polynomials dream of symmetric curves?
, Foundations of Computational Mathematics (2016) 16:1697-1736, doi: 10.1007/s10208-016-9313-0. Also preprint arXiv math.1511.09175.
A. Martínez-Finkelshtein, G. Silva, Critical measures for vector energy: global structure of trajectories of quadratic differentials
, Advances in Mathematics 302 (2016), 1137-1232. Also preprint arxiv math.1509.06704.
A. Martínez-Finkelshtein, D. Ramos-López, and D. Robert Iskander, Computation of 2D Fourier transforms and diffraction integrals using Gaussian radial basis functions
, Applied and Computational Harmonic Analysis 43 (3) (2017), 424-448.
A. Martínez-Finkelshtein, E. A. Rakhmanov, R. Orive, Phase transitions and equilibrium measures in random matrix models
, Comm. Math. Physics 333 (3) (2015), 1109-1173. doi 10.1007/s00220-014-2261-0. Also preprint arXiv math.1302.3647.
A. Martinez-Finkelshtein, E. A. Rakhmanov, Critical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomials
, Comm. Math. Physics 302, 53-111 (2011). Also preprint arXiv:0902.0193.
Current Ph.D. Students
Ana Belen Castaño, University of Almeria
Former Ph.D. Students
Juan José Moreno Balcázar, "Analytic properties of sontinuous Sobolev orthogonal polynomials" (coadvised with Miguel Piñar), October 6, 1997, University of Almeria.
Pedro Martínez Gonzalez, "Methods of study of the zero asymptotics of special functions" (coadvised with Alejandro Zarzo), July 4, 2001, University of Almeria.
Pedro Lopez Artés, "Entropies, potentials and linearization of hypergeometric polynomials" (coadvised with Jesús Sánchez Dehesa), April 9, 2002, University of Almeria.
Joaquín Sánchez Lara, "Entropies of orthogonal polynomials", July 2005, University of Almeria.
Vítor Luís Sousa, "The Riemann-Hilbert Method Applied to the Theory of Orthogonal Polynomials" (coadvised with Ana Foulquié), University of Aveiro, January 17, 2011.
Darío Ramos López, "Mathematical modelling in biomedical optics and ophthalmology", University of Almería, May 12, 2014, University of Almeria.