My main research interests lie in the areas of numerical analysis, scientific computing and computational physics. Currently I work developing numerical methods for problems arising in the computational simulation of magnetically confined plasmas. I have also interest in the application of integral equation techniques for the study of time domain wave propagation, in the applications and theoretical development of the Boundary Element Method (BEM) and the Hybridizable Discontinuous Galerkin Method (HDG), and in formulations that involve the coupling of integral and partial differential equations.
My detailed resume can be downloaded below
I was born and raised in Mexico City. I got a B.Sc. in Physics (under the supervision of Iouri N. Skiba ) and a M.Sc. in Mathematics (under the supervision of Antonio Capella) both from the National Autonomous University of Mexico (UNAM). I graduated with a Ph. D. in Applied Mathematics from the University of Delaware, where I studied under the supervision of the late Francisco-Javier Sayas. Between 2016 and 2020 I was a Postdoctoral Associate at the Courant Institute of Mathematical Sciences, where my mentor was Antoine Cerfon.
In 2018, as part of the Hispanic Heritage Month celebration of the contributions of Latinx and Hispanic mathematicians, I was featured by lathisms.org as a prominent early-career Hispanic mathematician. I am humbled and thankful for the honor.
Articles and pre-prints
- "Time-domain boundary integral formulations for combined-type boundary conditions in linear thermoelasticity".
With George Hsiao (In preparation)
- "Quantifying the effect of current variability on free boundary magnetic equilibrium computations in Tokamaks".
With Howard Elman and Jiaxing Liang (In preparation)
- "A priori and a posteriori error analysis of an HDG method for semi-linear elliptic problems in curved domains".
With Néstor Sánchez and Manuel Solano (Submitted). (arXiv:1911.12298)
- "Adaptive hybridizable discontinuous Galerkin discretization of the Grad-Shafranov equation by extension from subdomains".
With Antoine Cerfon and Manuel Solano (Computer Physics Communications, Vol. 255, pp.107239, 2020. doi:10.1016/j.cpc.2020.107239 (arXiv:1903.01724)
- "Time-domain boundary integral methods in linear thermoelasticity".
With George Hsiao (Dedicated to the memory of Francisco-Javier Sayas) (SIAM Journal of Mathematical Analysis, 52(3),2463-2490, 2020. doi:10.1137/19M1298652). (arXiv:1910.04884)
- "A Hybridizable Discontinuous Galerkin solver for the Grad-Shafranov equation".
With Manuel Solano (Computer Physics Communications. Vol. 235, pp 120-132, 2019. doi: 10.1016/j.cpc.2018.09.013). (arXiv:1712.04148)
- "Pseudo-spectral collocation with Maxwell polynomials for kinetic equations with energy diffusion".
With Antoine Cerfon (Plasma Physics and Controlled Fusion. 60(2): 025018, 2018. doi: 10.1088/1361-6587/aa963a) (arXiv:1708.09031)
- "Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid".
With Thomas Brown, and Francisco-Javier Sayas. (ESAIM: Mathematical Modelling and Numerical Analysis. Vol. 52, No. 2, pp. 423–455, 2018. doi:10.1051/m2an/2017045) (arXiv:1612.04063)
- "A time-dependent wave-thermoelastic solid interaction".
With George Hsiao, Francisco-Javier Sayas, and Richard Weinacht (IMA Journal of Numerical Analysis, 39(2):924–956, 04 2018. doi: 10.1093/imanum/dry016). (arXiv:1609.06330)
- "Symmetric Boundary-Finite Element discretization of time dependent acoustic scattering by elastic obstacles with piezoelectric behavior".
With Francisco-Javier Sayas. (Journal of Scientific Computing, Vol. 70, No. 3, 2017. pp. 1290--1315. doi: 10.1007/s10915-016-0281-y) (arXiv:1603.00289)
- “A new and improved analysis of the time domain boundary integral operators for acoustics”
With Matthew Hassell, Tianyu Qiu and Francisco-Javier Sayas. (Journal of Integral Equations and Applications, Vol 29, No. 1, 2017. doi: 10.1216/jie-2017-29-1-107) (arXiv:1512.02919)
- "Boundary and coupled boundary-finite element methods for transient wave-structure interaction."
With George Hsiao and Francisco-Javier Sayas. (IMA Journal of Numerical Analysis, Vol. 37, No. 1, 2016. pp. 237--265. doi: 10.1093/imanum/drw009) (arXiv:1509.01713)
- "A fully discrete Calderón calculus for the two-dimensional elastic wave equation."
With Víctor Domínguez and Francisco-Javier Sayas. (Computers and Mathematics with Applications , Vol. 69, No. 7. 2015. pp. 620--635. doi: 10.1016/j.camwa.2015.01.016)(arXiv:1409.7653)
Conference proceedings and other publications
- "The Mathematics of Cathleen Synge Morawetz".
With Irene Gamba, Leslie Greengard, Kevin Payne, Christina Sormani and Terence Tao. (Notices of the American Mathematical Society, 65(07):764–778, Aug 2018.)
- "FEM-BEM coupling for transient acoustic scattering by thermoelastic obstacles."
With George Hsiao, Francisco-Javier Sayas and Richard Weinacht. For WAVES 2017 at the University of Minnesota.
- "Semidiscrete evolution of elastic waves in a piezoelectric solid."
With Thomas Brown and Francisco-Javier Sayas. For WAVES 2017 at the University of Minnesota.
- "A system of boundary integral equations for transient wave-structure interaction."
With Francisco-Javier Sayas. For WAVES 2015 at the Karlsruhe Institute of Technology, Germany.
Fall 2020: MATH 125 (Calculus I) Section 007
IMPORTANT: The class is scheduled to meet online at the beginning of the semester and transition into presential lectures following a data-based approach which will include expert advice from faculty in our Zuckerman College of Public Health. After the Thanksgiving break, the class will switch back to online instruction from November 26, 2020 until December 9, 2020.
- Meeting time: Tuesdays and Thursdays 11:00 A.M. --- 12:15 P.M.
- Meeting place: Emil W. Haury Anthropology Building, Room 216. (NOTE: Due to COVID-19 related restrictions, the class will be online until further notice.)
- Office hours: Tuesday: 9:30 AM - 11:00 AM // Thursday 12:30 PM - 2:00 PM
You can find answers for frequently asked questions (required textbook, recommended/allowed calculators, WebAssign, etc.) and plenty of useful resources (reference sheets, reviews, videos, practice exams, etc.) in the