# Andrei Martinez-Finkelshtein, Ph.D.

Professor of Mathematics

## Education

B.S. and M.A. in Mathematics (1986), Havana University, Cuba

Ph. D. in Mathematics (1991) State Moscow University "M.V. Lomonosov", Russia

## Biography

Dr. Martinez-Finkelshtein started teaching full-time at Baylor in January 2018. Before joining Baylor University, Andrei was a full professor of applied mathematics at the University of Almeria, Spain (1994-). He also taught at 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 (the University of South Florida and Vanderbilt University). He is a member of several professional societies and is currently the Program Director of the SIAM Activity Group "Orthogonal Polynomials and Special Functions" (its vice-chair in 2017-2019). He is also on the editorial board of six journals. He loves gadgets, and his hobbies include listening to music (and playing some), 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 modeling, in particular, in ophthalmology and vision science.

## Recent Selected Publications

- A. Martinez-Finkelshtein, R. Morales, D. Perales,
*Real roots of hypergeometric polynomials via finite free convolution*, International Mathematics Research Notices, Volume**2024**, Issue 16, August 2024, Pages 11642–11687, https://doi.org/10.1093/imrn/rnae120. Also, preprint arXiv:2309.10970. - A. Martínez-Finkelshtein, R. Orive, J. Sánchez-Lara,
*Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials*, Constructive Approximation**58**(2023), 271–342, DOI 10.1007/s00365-022-09609-x. - M. Hunziker, A. Martinez-Finkelshtein, T. Poe, B. Simanek,
*Poncelet-Darboux, Kippenhahn, and Szegő: interactions between projective geometry, matrices and orthogonal polynomials*, Journal of Mathematical Analysis and Applications**511**(1), 126049. - M. Hunziker, A. Martinez-Finkelshtein, T. Poe, B. Simanek,
*On foci of ellipses inscribed in cyclic polygons*, in F. Gesztesy, A. Martinez-Finkelshtein (eds.), "From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory", Operator Theory: Advances and Applications 285, https://doi.org/10.1007/978-3-030-75425-9_12, 2021, pages 213-238. - A. Martinez-Finkelshtein, G. Silva,
*Spectral curves, variational problems, and the hermitian matrix model with external source*, Comm. Math. Physics 383 (3), (2021) 2163-2242. - G. M. Castro-Luna, A. Martínez-Finkelshtein, D. Ramos-López,
*Robust keratoconus detection with Bayesian network classifier for Placido-based corneal indices*, Contact Lens & Anterior Eye 43 (2020), 366-372. - 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. 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.

**Teaching at Baylor**

- Fall 2018: MTH 2321 (Calculus III) and MTH 4329 (Complex Variables).
- Spring 2019: MTH 5V92 (Orthogonal Polynomials, Theory and Applications)
- Fall 2019: MTH 4326 (Advanced Calculus) and MTH 4329 (Complex Variables).
- Spring 2020: MTH 2321 (Calculus III).
- Fall 2020: MTH 4326 (Advanced Calculus I) and MTH 4329 (Complex Variables).
- Spring 2021: 4327 (Advanced Calculus II).
- Summer 2021: MTH 6V23 (Orthogonal Polys Random Matrices) and MTH 1321 (Calculus I)
- Fall 2021: MTH 1321 (Calculus I)
- Spring 2022: MTH 6322 (Approximation Theory)
- Fall 2022: MTH 2321 (Calculus III) and MTH 4329 (Complex Variables).
- Spring 2023: MTH 5V92 (Orthogonal Polynomials, Theory and Applications)
- Summer 2023: MTH 6V23 (Logarithmic Potential Theory)
- Fall 2023: MTH/CSI 3324 (Numerical methods) and MTH 4329 (Complex Variables)
- Spring 2024: MTH 6V23 (Asymptotic Analysis)
- Summer 2024: MTH 6V23 (Riemann Surfaces)

## Current Ph.D. Students

- Rafael Morales.
- Alejandro Quintero.
- James Kessinger.
- Jesus Hernandez Rodriguez.