Liliana Borcea

Professor of Applied Mathematics (starting July 2024)

200 Mudd, MC 4701
500 W. 120th St.
New York, NY 10027

Research Interests

Wave propagation in random media with applications to wave based imaging and free space optical communications; Inverse problems for hyperbolic, elliptic and parabolic partial differential equations; , Data driven reduced order modeling and applications to inverse problems; Scientific computing

Liliana Borcea will join the Department of Applied Physics and Applied Mathematics at Columbia Engineering in July 2024 as a professor of Applied Mathematics.

Her research interests are in applied mathematics, with particular interests in wave propagation in random media with applications to wave-based imaging and free space optical communications; inverse problems for hyperbolic, elliptic, and parabolic partial differential equations; and data-driven reduced order modeling and applications to inverse problems.

Professor Borcea earned her undergraduate degree in Applied Physics from the University of Bucharest in Romania and her PhD in Scientific Computing and Computational Mathematics (SCCM) from Stanford University. Following a one-year postdoctoral fellowship in the Department of Applied Mathematics at Caltech, she joined the faculty in the Department of Computational and Applied Mathematics at Rice University in 1996 and was named the Noah Harding Professor in 2007. She then joined the Mathematics faculty at the University of Michigan, Ann Arbor, where she has been the Peter Field Collegiate Professor of Mathematics since 2013.

Professor Borcea was recognized as the AWM-SIAM Sonia Kovalevsky Lecturer for 2017, selected "for her distinguished scientific contributions to the mathematical and numerical analysis of wave propagation in random media, array imaging in complex environments, and inverse problems in high-contrast electrical impedance tomography, as well as model reduction techniques for parabolic and hyperbolic partial differential equations." She is a member of the 2018 class of SIAM Fellows and was elected to the American Academy of Arts and Sciences in 2023.

Professional Experience

Starting July 2024: Columbia University, Department of Applied Physics and Applied Mathematics
Professor of Applied Mathematics

2013-2024: University of Michigan, Department of Mathematics
Peter Field Collegiate Professor

1996-2013: Rice University, Department of Computational and Applied Mathematics
Noah Harding Professor, 2007-2013
Associate Professor, 2001-2007
Assistant Professor, 1996-2001

Research Experience

1996-1997 California Institute of Technology, Applied Mathematics
NSF Postdoctoral fellow on leave from Rice University

1991-1992 NASA Ames, Moet Field, California
Research assistant

1987-1990 IPIM 13 Decembrie, Sibiu, Romania
Computer programmer

Education

Ph.D. (1996) Stanford University. Scientific Computing and Computational Mathematics.

M.S. (1994) Stanford University. Scientific Computing and Computational Mathematics.

B.S. (1987) University of Bucharest, Romania. Department of Applied Physics.

Honors & Awards

2023 Election to the American Academy of Arts and Sciences

2022 Rothschild Distinguished Visiting Fellowship (for the year 2023), Isaac Newton Institute of

Mathematical Sciences, Cambridge University, UK

2022 Plenary Speaker, SIAM Imaging Science Conference

2020 Elected to the SIAM Board of Trustees for two terms: (2021-2023) and (2024-2025).

2019 Editor in chief, SIAM Journal Multiscale Modeling and Simulations. First term: (2019-2022)

and reappointed for second term (2023-2025)

2018 SIAM Fellow

2018 Distinguished Women in Mathematics lecture, University of Texas, Austin

2017 The AWM-SIAM Sonia Kovalevsky prize

2015 Simons Fellow in Mathematics

2014 Elected to the SIAM Council. Served two terms: 2014-2017 & 2017-2020

2013 Peter Field Collegiate chair, University of Michigan.

2012 SIAM SIGEST award.

2010 NSA Research Professorship, MSRI Berkeley

2007 Noah Harding chair, Rice University

2007 Plenary speaker, AMS West Section Meeting, Tucson, AZ.

2004 Invited topical speaker, SIAM Annual meeting, Portland, OR

1996-99 NSF Mathematical Sciences Postdoctoral Research Fellowship

1994-96 NSF Graduate Research Traineeship

1992-93 Stanford NASA Ames Global Change fellowship

1983 Laureate of the national contest \Traian Lalescu" between all Romanian Physics Universities

1982 Laureate of the Romanian national olympiad in Physics

Selected Publications

1. L. Borcea, J. Garnier, A. Mamonov, J Zimmerling, Waveform inversion with a data driven estimate of the internal wave, SIAM J. Imaging Science, 16 (1), 2023, p. 280-312.

2. L. Borcea, J. Garnier, K. Solna, Paraxial wave propagation in random media with long-range correlations, SIAM J. Applied Math, 83 (1), 2023, p. 25-51.

3. L. Borcea, J. Garnier, A. Mamonov, J. Zimmerling, Waveform inversion via reduced order modeling, Geophysics 88 (2), 2023, R175-R191.

4. A. Mamonov, L. Borcea, J. Garnier, J. Zimmerling, Velocity estimation via model order reduction, Second International Meeting for Applied Geoscience & Energy, p. 752-756, 2022.

5. L. Borcea, J. Garnier, A. Mamonov, J. Zimmerling, Reduced order model approach for imaging with waves, Inverse Problems, 38(2), 2022, p. 025004, 40 pp.

6. L. Borcea, V. Druskin, J. Zimmerling, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientic Computing, 89(1), 2021, p.1{36.

7. L. Borcea, J. Garnier, Imaging in random media by two-point coherent interferometry, SIAM J. Imaging Science, 14(4), 2021, p. 1635-1668

8. L. Borcea, J. Garnier, K. Solna, Onset of energy equipartition among surface and body waves, Proceedings of the Royal Society A, 477, 2021, 20200775, 28pp.

9. L. Borcea, B. Riviere, Y. Wang, Nonoverlapping domain decomposition method with preconditioner from asymptotic analysis of steady flow in high contrast media, International Journal of Computer Mathematics, 98(10), 2021, p. 2008{2024.

10. L. Borcea, J. Garnier, K. Solna, Multimode communication through the turbulent atmosphere, JOSA A, 37(5), 2020, p. 720-730.

11. L. Borcea, V. Druskin, A. Mamonov, S. Moskow, M. Zaslavsky, Reduced order models for spectral domain inversion: embedding into the continuous problem and generation of internal data, Inverse Problems 36(5), 2020, p. 055010, 24pp.

12. L. Borcea, E Karasmani, C. Tsogka, Incoherent source localization in random acoustic waveguides, Waves in Random and Complex Media, 30 (1), 2020, p. 81-106.

13. L. Borcea, V. Druskin, A. Mamonov, M. Zaslavsky, J Zimmerling, Reduced Order Model Approach to Inverse Scattering, SIAM J. Imaging Science, 13(2), 2020, p. 685-723.

14. L. Borcea, J. Garnier, High-resolution interferometric synthetic aperture imaging in scattering media, SIAM J. Imaging Science, 13(1), 2020, p. 291-316.

15. L. Borcea, J. Garnier, Wave propagation in randomly perturbed weakly coupled waveguides, SIAM Multiscale Modeling Simul., 18(1), 2020, p. 44-78.