Research & Publications

My main interests are in geometric measure theory, PDE, calculus of variations and harmonic analysis. In particular, I am currently interested in the regularity and structure of area-minimizing surfaces. I am also interested in Whitney-type interpolation/extension problems in Sobolev spaces with low regularity, the singular structure of measures satisfying differential constraints, the properties of anisotropic BV spaces, and, more recently, regularity questions in free boundary problems.

Publications/preprints:

• Higher codimension area-minimizing currents mod(q): structure of singularities near (m-1)-invariant cones (joint w/ C. De Lellis & P. Minter, preprint, 2024)

• Sobolev extension in a simple case (joint w/ M. Drake, C. Fefferman & K. Ren, accepted,  Adv. Nonlin. Stud., 2024)

• Flat interior singularities for area almost-minimizing currents (joint w/ M. Goering, preprint, submitted, 2023)

• Variational integrals on Hessian spaces: partial regularity for critical points (joint w/ A. Bhattacharya, preprint, submitted, 2023)

• Rectifiability of flat singular points for area-minimizing mod(2Q) hypercurrents (IMRN, 2023)

• The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points (joint w/ C. De Lellis, preprint, submitted, 2023)

• The fine structure of the singular set of area-minimizing integral currents II: rectifiability of flat singular points with singularity degree larger than 1 (joint w/ C. De Lellis, preprint, submitted, 2023)

• The fine structure of the singular set of area-minimizing integral currents III: frequency 1 flat singular points and $\mathcal{H}^{m−2}$-a.e. uniqueness of tangent cones (joint w/ C. De Lellis & P. Minter, preprint, submitted, 2023)

• An upper Minkowski bound for the interior singular set of area minimizing currents (CPAM, 2021)

• Higher integrability for measures satisfying a PDE constraint (joint w/ A. Arroyo-Rabasa, G. De Philippis, J. Hirsch & F. Rindler, accepted, Trans. Amer. Math. Soc., 2021)

• Continuity and canceling operators of order $n$ on $\mathbb{R}^n$ (joint w/ B. Raiță, Calc. Var. PDE, 2019)

• A look into some of the fine properties of functions with bounded $\mathcal{A}$-variation (joint w/ A. Arroyo-Rabasa, preprint, 2019)