I am an Assistant Professor (tenure-track) at the Department of Mathematics of Johns Hopkins University, starting from 2023.
I was an NSF Postdoc and L.E. Dickson Instructor at the University of Chicago since August 2019. My mentor was Prof. Carlos Kenig.
From September 2018 to July 2019, I was a member at the Institute for Advanced Study during the
Sepcial Year on Variational Methods in Geometry
.
My mentor was
Prof. Camillo De Lellis
.
In June 2018 I graduated from the University of Washington, and my advisor was
Prof. Tatiana Toro.
You can find my CV
here
.
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 area-minimizing 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.
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A Note on the Critical Set of Harmonic Functions Near the Boundary
with Carlos Kenig
Submitted on arXiv
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Elliptic Operators in Rough Sets, and the Dirichlet Problem with Boundary Data in Hölder Spaces
with Mingming Cao, Pablo Hidalgo-Palencia, José María Martell, Cruz Prisuelos-Arribas
Submitted on arXiv
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Examples of non-Dini domains with large singular sets
with Carlos Kenig
Advanced Nonlinear Studies Special Issue: In honor of David Jerison (2023) 23 no. 1
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Expansion of Harmonic Functions Near the Boundary of Dini Domains
with Carlos Kenig
Rev. Mat. Iberoam. (2022) 38:2117-2152
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Elliptic Measures for Dahlberg-Kenig-Pipher Operators: Asymptotically Optimal Estimates
with Simon Bortz, Tatiana Toro
Math. Ann. (2023) 385:881-919
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Boundary Unique Continuation on Dini Domains and the Size of the Singular Set
with Carlos Kenig
Arch. Ration. Mech. An. (2022) 245:373-374
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Optimal Poisson Kernel Regularity for Elliptic Operators with Hölder-continuous Coefficients in Vanishing Chord-arc Domains
with Simon Bortz, Tatiana Toro
J. Funct. Anal. (2023) 285 no. 5.
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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) 31:325-401
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Two Phase Free Boundary Problem for Poisson Kernels
with Simon Bortz, Max Engelstein, Max Goering, Tatiana Toro
Indiana U. Math. J. (2022) 71:251-306
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Dirichlet Energy-minimizers with Analytic Boundary
with Camillo De Lellis
Indiana U. Math. J. (2023) 72:1367-1428
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Dirichlet Problem in Domains with Lower Dimensional Boundaries
with Joseph Feneuil, Svitlana Mayboroda
Rev. Mat. Iberoam. (2021) 37:821-910
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Square Function Estimates, BMO Dirichlet Problem, and Absolute Continuity of Harmonic Measure on Lower-dimensional Sets
with Svitlana Mayboroda
Anal. PDE (2019) 12:1843-1890
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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
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Boundary Rectifiability and Elliptic Operators with W^{1,1} Coefficients
with Tatiana Toro
Adv. Calc. Var. (2021) 14:37-62
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BMO Solvability and the A-infty Condition of the Elliptic Measure in Uniform Domains
J. Geom. Anal. (2018) 28:866-908
