I am a postdoctoral investigator at the Universitat Autònoma de Barcelona, working with Xavier Tolsa. I will be joining the Department of Mathematics at the University of Pittsburgh as a tenure-track assistant professor in August 2024. I have obtained my Ph.D in mathematics from the University of Minnesota in May 2021, my thesis having garnered the 2021 Outstanding Thesis award from the department.  My doctoral advisor was Svitlana Mayboroda. I was born and raised in Portoviejo, Manabí, Ecuador. This site records my professional journey in mathematics. I also enjoy composing relaxing instrumental music for the piano.

Papers and preprints

• The $A_\infty$ condition, ε-approximators, and Varopoulos extensions in uniform domains (with S. Bortz, and O. Tapiola, and X. Tolsa). To appear in Journal of Geometric Analysis. arXiv version

• Critical perturbations for second order elliptic operators. Part II: Non-tangential maximal function estimates (with S. Bortz, and S. Hofmann, and J.L. Luna García, and S. Mayboroda). Archive for Rational Mechanics and Analysis, Volume 248, Number 31 (2024). arXiv version

• On an almost sharp Liouville type theorem for fractional Navier-Stokes equations (with D. Chamorro). To appear in Publicacions Matemàtiques. arXiv version

• $L^p$-solvability of the Poisson-Dirichlet problem and its applications to the regularity problem (with M. Mourgoglou and X. Tolsa). arXiv version 

• Applications of the landscape function for Schrödinger operators with singular potentials and irregular magnetic fields. Advances in Mathematics, Volume 445 (2024).  arXiv version 

• Generalized Carleson perturbations of elliptic operators and applications (with J. Feneuil). Transactions of the American Mathematical Society, Volume 375, Number 11 (2022) 7553-7599. arXiv version  

• Carleson perturbations of elliptic operators on domains with low dimensional boundaries (with S. Mayboroda).  Journal of Functional Analysis, Volume 280, Number 8 (2021). arXiv version 

• Critical perturbations for second-order elliptic operators. Part I: Square function bounds for layer potentials (with S. Bortz, and S. Hofmann, and J.L. Luna García, and S. Mayboroda). Analysis & PDEs, Volume 15, Number 5 (2022) 1215-1286. arXiv version

• Failure to slide: A brief note on the interplay between the Kenig-Pipher condition and absolute continuity of elliptic measures. arXiv version 

• Optimal Stefan Problem (with U. Abdulla). Calculus of Variations and Partial Differential Equations, Volume 59, Number 61 (2020) arXiv version, journal version.

• Exponential decay estimates for fundamental solutions of Schrödinger-type operators (with S. Mayboroda). Transactions of the AMS, Volume 372, Number 6 (2019) 4313–4357 arXiv version, journal version.

• Optimal Control of the Multiphase Stefan Problem (with U. Abdulla). Applied Mathematics and Optimization, Volume 80, 479-513 (2019), journal version.

Scientific posters, and slides, recordings or manuscripts for talks

• Generalized Carleson perturbations of elliptic operators and applications. An online talk given on November 2020 for the Analysis seminar at SUNY-Albany.

• Generalized Carleson perturbations of elliptic operators and applications. An online talk given on November 2020 for the Analysis seminar at the Universidad Autónoma de Madrid-ICMAT (recording (given in spanish)).

• Additive and scalar-multiplicative Carleson perturbations of elliptic operators on domains with lower dimensional boundaries. An online talk given on September 2020 for the Analysis seminar at the University of Alabama.

• Additive and scalar-multiplicative Carleson perturbations of elliptic operators on domains with lower dimensional boundaries. An online talk given on September 2020 for the HA-GMT-PDE Seminar at the University of Minnesota. (Recording)

• Carleson perturbations of elliptic operators on domains with higher-codimensional boundaries. A poster presented on March 2020 at the Analysis, Dynamics, Geometry, and Probability workshop in the honor of Chris Bishop's 60th birthday at Stony Brook University, Stony Brook, New York.

• Exponential decay of Green’s functions and the Filoche-Mayboroda landscape function. A poster presented on February 2020 at the Simons Collaboration on Localization of Waves Annual Meeting 2020, Manhattan, New York.

• Exponential Decay Estimates for Fundamental Solutions of Schrödinger-type Operators. A poster presented on September 2019 at Analysis in Missouri: a Midwestern symposium, Columbia, Missouri.

• Exponential Decay Estimates for Fundamental Solutions of Schrödinger-type Operators.  A poster presented on May 2019 at the Short course and workshop: Quantum mechanics and semiconductors, Santa Barbara, California.

• Exponential Decay Estimates for Fundamental Solutions of Schrödinger-type Operators.  A poster presented on January 2019 at the Workshop on Spectral Properties of Disordered Systems, Paris, France.

• Carleson perturbations of elliptic operators on domains with higher co-dimensional boundaries.  A talk given on April 2019 for the AMS Special Session on the Regularity theory of PDEs and Calculus of Variations on Domains with Rough Boundaries.

• Carleson perturbations of elliptic operators on domains with higher co-dimensional boundaries.  A talk given on 03/30/2019 for the Geometric and Harmonic Analysis 2019 conference at the University of Connecticut, Storrs, Connecticut.

• An introductory talk on the exponential decay of some solutions to Schrödinger operators. A talk given on 09/26/2018 for the AMS Introduction to Research seminar at the University of Minnesota, Minneapolis, Minnesota. This talk was given at a very elementary level. 

• Schrödinger operator: optimal decay of fundamental solutions and boundary value problems. A talk given on 07/17/2018 for the Research Program in Mathematics at the Park City Mathematics Institute, Park City, Utah. Similar to the talk given as part of my oral examination.

• Boundary value problems for second-order elliptic operators with lower order terms. A talk given on 05/04/2018 as part of my oral examination for the doctoral program in mathematics at the University of Minnesota, Minneapolis, Minnesota.

• Exponential decay estimates for fundamental solutions of Schrödinger-type operators. A talk given on 04/21/2018 in the AMS Special Session on Regularity of PDEs on rough domains, at the April 21-22 AMS Sectional Meeting in Boston, Massachusetts. 

• The failure of the DeGiorgi-Nash-Moser regularity theory for second-order elliptic equations at the critical exponent case. A talk given on 11/17/2017 in the Analysis & PDE Working Seminar at the University of Minnesota, Minneapolis, Minnesota.

• The exponential decay of fundamental solutions to certain Schrödinger operators. A poster presented on 05/16/2017 in the 'Recent Developments in Harmonic Analysis' Poster session, at the MSRI, Berkeley, California.

• The Characterization of Sobolev functions as Absolutely Continuous on a.e. Line, and Applications. A talk given on 11/16/2016 in the Student PDE Seminar at the University of Minnesota, Minneapolis, Minnesota.

External Links

• My profile in ResearchGate.

• My profile in Google Scholar.

• School of Mathematics at the University of Minnesota.

• Department of Mathematics at the Universitat Autonoma de Barcelona. 

• Conference HAPDEGMT in Bilbao 2023.