Mariana Smit Vega Garcia, PhD

Professor

Research Interests:

Analysis, Partial Differential Equations, Geometric Analysis

About

I was born and raised in Sao Paulo, Brazil, where I obtained my bachelor's and master's in Mathematics at the Universidade de Sao Paulo.

After moving to the US for graduate school I obtained my PhD from Purdue University in 2014.

Afterwards, I did a post-doc in Germany (at Heinrich Heine University Dusseldorf and the University of Duisburg-Essen), and spent two months as a postdoctoral fellow at the Mittag-Leffler Institute, in Sweden. In 2016 I returned to the US for a post-doc at UW, where I continued working with free boundary problems and expanded my research to geometric measure theory and harmonic analysis. 

In my free time, I love to hike, travel, play with my dogs, watch soccer, read books, go to the symphony and enjoy good food with friends. 

Educational & Professional Experience:

  • PhD Purdue University, 2014.
  • Wissenschaftliche Mitarbeiterin (post-doc), Heinrich Heine Universität and Universität Duisburg-Essen, 2014-2016.
  • Institut Mittag-Leffler Postdoctoral fellow, September-October 2014.
  • Acting Assistant Professor, UW, 2016-2018.

Recent Publications

- Variable-coefficient parabolic theory as a high-dimensional limit of elliptic theory
B. Davey & M. Smit Vega Garcia
Calc. Var. 63, 40 (2024).
arXiv:2304.10731v1

- Two-phase almost minimizers for a fractional free boundary problem
M. Allen & M. Smit Vega Garcia
Nonlinear Differ. Equ. Appl. 31, 45 (2024).
arXiv:2308.06357

- An Almgren monotonicity formula for discrete harmonic functions
M. Smit Vega Garcia & S. Steinerberger
arXiv:2311.11887, 2023.

- Mesas of Stirling permutations
N. Gonzalez, P. E. Harris, G. R. Kirby, M. Smit Vega Garcia & B. E. Tenner
to appear on "Journal of Combinatorics."
arXiv:2306.12158, 2023

- Pinnacle sets of signed permutations
N. Gonzalez, P. E. Harris, G. R. Kirby, M. Smit Vega Garcia & B. E. Tenner
Discrete Mathematics, Volume 346, Issue 7, 2023.
arXiv:2301.02628v1

- Branch Points for (Almost-)Minimizers of Two-Phase Free Boundary Problems
G. David, M. Engelstein, M. Smit Vega Garcia & T. Toro,
Forum of Mathematics, Sigma, 11, E1, 2023.
ArXiv:2204.05367

- An overview of Almost Minimizers of Bernoulli-Type Functionals
M. Smit Vega Garcia
A3N2M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models, Proceedings of the 50th John H. Barrett Memorial Lectures, IMA Volumes in Mathematics and its Applications, volume 165, 2023, Springer.

- Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals
G. David, M. Engelstein, M. Smit Vega Garcia & T. Toro
Mathematische Zeitschrift, 299(3), 2131-2169, 2021.
arXiv:1909.05043

- On a Bernoulli-type overdetermined free boundary problem
M. Akman, A. Banerjee & M. Smit Vega Garcia
Ann. Fenn. Math., vol. 46, no. 2, pp. 601-618, Aug. 2021
arXiv:1911.02801

- The fractional unstable obstacle problem
M. Allen & M. Smit Vega Garcia
Nonlinear Analysis, Vol 193, April 2020
arXiv:1811.12497

- Almost minimizers for the thin obstacle problem with variable coefficients
S. Jeon, A. Petrosyan & M. Smit Vega Garcia
arXiv:2007.07349
2020

Selected Awards & Honors:

  • NSF Analysis RUI Grant. Title: "Topics in Free Boundary Problems." Award  from 09/01/2024 - 08/31/2027. Award amount: $208,780.
  • NSF Analysis Standard Grant. Title: "Analysis and Geometry of Free Boundaries." Award from 08/15/2021 – 05/31/2025.  Award amount: $190,337.00.
  • Karen EDGE Fellowship (2024-2027).
  • Peter J. Elich Excellence in Teaching Award, 2023.
  • NSF Conferences and Workshops in the Mathematical Sciences. Conference: "Geometry of Measures and Free Boundaries, a conference in honour of Tatiana Toro." Funded, DMS 2403698 (2023-2024).
  • NSF Conferences and Workshops in the Mathematical Sciences. Conference: "PDE in Moab: Advances in Theory and Application." Funded, DMS 2350128 (2024).
  • Simons Laufer Mathematical Sciences Institute (SLMath, formerly MSRI) - 2023 Summer Research in Mathematics program.
  • Committee for the Education of Teaching Assistants teaching award, Purdue University. 
  • Purdue University Math Department Excellence in Teaching award for 2011-12.
  • Graduated with honors, Universidade de Sao Paulo, 2006.