Faculty Profile for Dr. Nestor D Guillen Matheus

profile photo for Dr. Nestor D Guillen Matheus
Dr. Nestor D Guillen Matheus
Associate Professor — Mathematics
phone: (512) 245-3934

Biography Section

Biography and Education

Nestor Guillen was born and raised in Valera, a town in the Venezuelan Andes. He has been at Texas State since 2019. Before that, his academic homes (in reverse chronological order) where UMass and UCLA, with shorter stays at the Fields Institute, the Mathematical Sciences Research Institute, and the Institute for Advanced Study. He obtained his PhD at UT Austin in 2010 and his Licenciatura en Matemáticas at Universidad Simón Bolívar in 2006.

Teaching Interests

I am interested in teaching both mathematics major as well as non-majors in STEM areas. A long term goal of mine is to incorporate computational and visual tools like interactive Python / OpenGL / Tablets in my instruction at all levels.

Research Interests

My research lies broadly in the analysis of nonlinear partial differential equations, including Monge-Ampère type equations (arising in geometry and optimal transport), Hamilton-Jacobi equations (arising in optimal control), and kinetic equations (arising in the study of plasmas). At present I am particularly interested in regularity estimates and how they might inform the design of new optimization and scientific computing algorithms.

Selected Scholarly/Creative Work

  • Guillen, N., & Schwab, R. W. (2019). Min–max formulas for nonlocal elliptic operators. Calculus of Variations and Partial Differential Equations, 58(6). https://doi.org/10.1007/s00526-019-1631-z
  • Guillen Matheus, N. D., & Gualdani, M. (2019). On $A_p$ weights and the Landau equation. Calculus of Variations and Partial Differential Equations. https://doi.org/10.1007/s00526-018-1451-6
  • Guillen, N., & Gualdani, M. P. (2022). Hardy’s inequality and the isotropic Landau equation. Journal of Functional Analysis, 283(6). https://doi.org/https://doi.org/10.1016/j.jfa.2022.109559
  • Guillen, N., Kim, I., & Mellet, A. (2022). A Hele-Shaw limit without monotonicity. Archive for Rational Mechanics and Analysis. https://doi.org/10.1007/s00205-021-01750-4
  • Guillen, N., & Kitagawa, J. (2020). Optimal transport and the Gauss curvature equation. Methods and Applications of Analysis, 27(Special Issue for the 60th Birthday of John Urbas), 387–404. https://doi.org/https://dx.doi.org/10.4310/MAA.2020.v27.n4.a5

Selected Awards

  • Award / Honor Recipient: CAREER, National Science Foundation. July 1, 2022 - Present
  • Award / Honor Recipient: Visiting Researcher at the Fields Institute Toronto, Canada. 2014
  • Award / Honor Recipient: Wall Memorial Fellowship. 2009
  • Award / Honor Recipient: Frank Gerth III Graduate Excellence Award. 2007

Selected Grants

  • Guillen Matheus, Nestor D. CAREER: Integro-differential and transport problems in partial differential equations, National Science Foundation, Federal, $498969. (Submitted: July 2021, Funded: July 1, 2022 - May 2027). Grant.
  • Guillen Matheus, Nestor D. Collaborative Research: The Structure of Nonlocal Operators and Applications, National Science Foundation, Federal, $135000. (Funded: 2017 - 2020). Grant.
  • Guillen Matheus, Nestor D. Geometric and analytic issues of nonlinear equations modeling non-local phenomena, National Science Foundation, Federal, $102000. (Funded: 2012 - 2016). Grant.

Selected Service Activities

Electronic Journal of Differential Equations
July 2022-Present
National Science Foundation Panel
National Science Foundation panel
Reviewer / Referee
Communications on Pure and Applied Mathematics
Reviewer / Referee
Calculus of Variations and Partial Differential Equations