Agosto 2024 - presente: 'Assistant Professor' en el Departamento de Matemáticas en la Universidad de Pittsburgh (Tenure-track)
Junio 2021 - Julio 2024: Investigador postdoctoral en la Universitat Autònoma de Barcelona bajo el premio ERC de Xavier Tolsa
Agosto 2015 - Mayo 2021: Ph.D en Matemáticas en la Universidad de Minnesota, bajo la dirección de Svitlana Mayboroda. Premio a la Tesis Doctoral Sobresaliente en Matemáticas (2021)
Agosto 2015 - Mayo 2018: M.S. en Matemáticas en la Universidad de Minnesota
Junio 2014 - Julio 2015: M.S. en Matemáticas Aplicadas por el Florida Institute of Technology
Agosto 2010 - Mayo 2014: B.S. en Ingeniería Aeroespacial y B.S. en Ciencias de las Matemáticas por el Florida Institute of Technology
Publicaciones:
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). Preprint.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
Tesis doctoral:
Título de la tesis. Boundary value problems for second-order elliptic equations and related topic.
Tesis defendida en la Universidad de Minnesota (2021).
Directora de tesis: Svitlana Mayboroda.
Cursos de verano para Amarun
La función paisaje y el principio de incertidumbre (2022).