Broadly speaking my work lies in the intersection of Geometric Measure Theory, Geometric Analysis, Harmonic Analysis, and PDEs.
I work on regularity problems of elliptic PDEs and generalized minimal submanifolds. In particular I am interested in the regularity of areaminimizing currents; unique continuation problems; the properties of the harmonic and elliptic measures and their relations to elliptic boundary value problem.
A complete list of my preprints can also be viewed on my arXiv page.

Expansion of Harmonic Functions Near the Boundary of Dini Domains
with Carlos Kenig
Submitted on arXiv

Elliptic Measures for DahlbergKenigPipher Operators: Asymptotically Optimal Estimates
with Simon Bortz, Tatiana Toro
Submitted on arXiv

Boundary Unique Continuation on Dini Domains and the Size of the Singular Set
with Carlos Kenig
Submitted on arXiv

Optimal Poisson Kernel Regularity for Elliptic Operators with Höldercontinuous Coefficients in Vanishing Chordarc Domains
with Simon Bortz, Tatiana Toro
Submitted on arXiv

Uniform Rectifiability and Elliptic Operators Satisfying a Carleson Measure Condition. Part II: The Large Constant Case
with Steve Hofmann, José María Martell, Svitlana Mayboroda, Tatiana Toro
(Combined with Part I of the series for publication) Geom. Funct. Anal. (2021) 31:325401

Two Phase Free Boundary Problem for Poisson Kernels
with Simon Bortz, Max Engelstein, Max Goering, Tatiana Toro
To appear on Indiana U. Math. J.

Dirichlet Energyminimizers with Analytic Boundary
with Camillo De Lellis
Submitted on arXiv

Dirichlet Problem in Domains with Lower Dimensional Boundaries
with Joseph Feneuil, Svitlana Mayboroda
Rev. Mat. Iberoam. (2021) 37:821910

Square Function Estimates, BMO Dirichlet Problem, and Absolute Continuity of Harmonic Measure on Lowerdimensional Sets
with Svitlana Mayboroda
Anal. PDE (2019) 12:18431890

Uniform Rectifiability and Elliptic Operators Satisfying a Carleson Measure Condition. Part I: The Small Constant Case
with Steve Hofmann, José María Martell, Svitlana Mayboroda, Tatiana Toro
Submitted on arXiv

Boundary Rectifiability and Elliptic Operators with W^{1,1} Coefficients
with Tatiana Toro
Adv. Calc. Var. (2021) 14:3762

BMO Solvability and the Ainfty Condition of the Elliptic Measure in Uniform Domains
J. Geom. Anal. (2018) 28:866908