I am a J.J. Sylvester assistant professor at Johns Hopkins University since July 2023. I got my Ph.D. at UT-Austin in May 2023 under the supervision of Luis Caffarelli and Francesco Maggi.
I am broadly interested in variational problems arising in partial differential equations and geometric measure theory.
I am currently on the job market for tenure track positions. Here is my CV.
Email : drestre1 at jhu dot edu
On the asymptotic properties of solutions to one-phase free boundary problems,
[ arxiv | journal ] with Max Engelstein, Zihui Zhao,
in preparation (2025).
Local collapsing and convergence properties in Gauss' capillarity theory,
[ arxiv | journal ] with Francesco Maggi, Michael Novack,
in preparation (2025).
Linear stability and convergence of diffused volume preserving mean curvature flow,
[ arxiv | journal ]
in preparation (2025).
On the Grad-Mercier equation and Semilinear Free Boundary Problems,
[ arxiv | journal ] with Luis Caffarelli, Antonio Farah,
submitted (2025).
Free boundary regularity for semilinear variational problems with a topological constraint,
[ arxiv | journal ] with Michael Novack, Anna Skorobogatova,
submitted (2024).
C^\infty regularity in semilinear free boundary problems,
[ arxiv | journal ] with Xavier Ros-Oton,
Mathematische Annalen, vol. 392, 3397--3446, (2025).
Asymptotic behavior of a diffused interface volume-preserving mean curvature flow,
[ arxiv | journal ] with Matteo Bonforte, Francesco Maggi,
submitted (2024).
A hierarchy of Plateau problems and the approximation of Plateau's laws via the Allen–Cahn equation,
[ arxiv | journal ] with Francesco Maggi, Michael Novack,
submitted (2023).
Plateau borders in soap films and Gauss' capillarity theory,
[ arxiv | journal ] with Francesco Maggi, Michael Novack,
submitted (2023).
Uniform stability in the Euclidean isoperimetric problem for the Allen–Cahn energy,
[ arxiv | journal ] with Francesco Maggi,
Analysis & PDE, vol. 17, no. 5, 1761--1830, (2024).
On the Morse Index of least energy nodal solutions for quasilinear elliptic problems,
[ arxiv | journal ] with Óscar Agudelo, Carlos Vélez,
Calculus of Variations and Partial Differential Equations, vol. 59, no. 59, 1--35, (2020).
Multiplicity results and qualitative properties for Neumann semilinear elliptic problems,
[ arxiv | journal ] with Óscar Agudelo, Santiago Correa, Carlos Vélez,
Journal of Mathematical Analysis and Applications, vol. 468, no. 1, 141--160, (2018).
Homogenization of Diffusion Processes on Scale-Free Networks,
[ arxiv | journal ] with Fernando Morales,
Electronic Journal of Differential Equations, vol. 2016, no. 282, 1--24, (2016).
Sep 2025: Geometric Analysis Seminar, Rutgers University.
May 2025: PDE in Barcelona Conference, Universitat de Barcelona.
Apr 2025: Analysis and Probability Seminar, Iowa State University.
Apr 2025: PDE-Applied Math Seminar, University of Maryland.
Apr 2025: Analysis Seminar, Columbia University.
Mar 2025: Virtual Analysis in PDE Seminar (VAPS), Virtual.
Feb 2025: Analysis Seminar, UC San Diego.
Jul 2024: AMS-UMI International Joint Meeting, Palermo.
Nov 2023: Prairie Analysis Seminar, Kansas State University.
Oct 2023: Workshop on Degenerate and Singular Diffusion, ICMAT (Spain).
Jun 2023: AIMS Conference, Wilmington (NC).
Apr 2023: Analysis Seminar, Carnegie Mellon University.
Mar 2023: Geometry & Analysis Seminar, Columbia University.
Jan 2022: MATRIX Institute Workshop, Creswick (Australia).
Oct 2022: SIAM Central States Annual Meeting, Oklahoma State University.
Apr 2022: PDE Seminar UAM-ICMAT, Universidad Autónoma de Madrid (UAM).