Research

Here is a link to my CV.

Papers and Preprints:

  • (with M. Egert and O. Saari) A Theorem of Fefferman, Kenig and Pipher Re-revisited. arXiv:2107.14217. (preprint)

  • (with T. Toro and Zihui Zhao) Elliptic measures for Dahlberg-Kenig-Pipher operators: Asymptotically optimal estimates. Math Ann. (preprint)

  • (with J. Hoffman, S. Hofmann, J.L. Luna Garcia, K. Nystrom) Carleson measure estimates for caloric functions and

parabolic uniformly rectifiable sets. To appear in Analysis and PDE. (preprint)

  • (with J. Hoffman, S. Hofmann, J.L. Luna Garcia, K. Nystrom) Corona Decompositions for Parabolic Uniformly Rectifiable Sets. arXiv:2103.12497. (preprint)

  • (with J. Hoffman, S. Hofmann, J.L. Luna Garcia, K. Nyström) On Big Pieces approximations of parabolic hypersurfaces. To appear in Ann. Acad. Sci. Fenn. Math. (preprint)

  • (with T. Toro, Z. Zhao) Optimal Poisson kernel regularity for elliptic operators with Holder-continuous coefficients in

vanishing chord-arc domains. arXiv:2010.03056. (preprint)

  • (with J. Hoffman, S. Hofmann, J.L. Luna Garcia, K. Nyström) Coronizations and big pieces in metric spaces.

To appear in Ann. Inst. Fourier. (preprint)

  • (with S. Hofmann, J.L. Luna Garcia, S. Mayboroda, B. Poggi) Perturbations for Second Order Elliptic Operators. Part I: Square function bounds for layer potentials. To appear in Analysis and PDE. (preprint)

  • (with M. Egert and O. Saari) Note on time-regularity for weak solutions to parabolic systems of p-Laplace type. Proc. Amer. Math. Soc. 149 (2021), no. 4, 1677–1685. (preprint)

  • (with M. Egert and O. Saari) Sobolev contractivity of gradient flow maximal functions. arXiv:1910.13150 (preprint)

  • (with M. Engelstein, M. Goering, T. Toro and Z. Zhao) Two Phase Free Boundary Problem for Poisson Kernels. To appear in IUMJ.

  • (with Olli Tapiola) ε-Approximability of Harmonic Functions in L^p Implies Uniform Rectifiability, Proc. Amer. Math. Soc. 147 (2019), no. 5, 2107-2121. (preprint)

  • (with Steve Hofmann) Quantitative Fatou Theorems and Uniform Rectifiability. To appear in Potential Anal. (preprint)

  • (with Max Engelstein) Reifenberg Flatness and Oscillation of the Unit Normal Vector. preprint arXiv:1708.05331. (Improved version with M. Goering, T. Toro and Z. Zhao is above)

  • (with Pascal Auscher, Moritz Egert and Olli Saari) Non-local self-improving properties: A functional analytic approach. Tunisian J. Math. 1 (2019), no. 2, 151-183. (preprint)

  • (with Pascal Auscher, Moritz Egert and Olli Saari) Non-local Gehring lemmas. To appear in J. Geom. Anal. arXiv:1707.02080.

  • (with Pascal Auscher, Moritz Egert and Olli Saari) On regularity of weak solutions to parabolic systems, J. Math. Pures Appl. (9) 121 (2019) 216–243. (preprint)

  • (with Murat Akman, Steve Hofmann and José Maria Martell) Rectifiability, interior approximation and Harmonic Measure, Ark. Mat. 57 (2019), no. 1, 1-22. (preprint).

  • (with Steve Hofmann) A singular integral approach to a two phase free boundary problem, Proc. Amer. Math. Soc. 144 (2016), no. 9, 3959-3973. (preprint).

  • (with Steve Hofmann) Harmonic measure and approximation of uniformly rectifiable Sets, Rev. Mat. Iberoam. (2016) (preprint).

Talks and Presentations:

  • AMS Western Sectional, October 23 2021.

  • AMS Central Sectional, October 2021.

  • PAW Seminar, September 2021.

  • Continuum Mechanics Seminar, U. Nebraska, September 2021.

  • HA-GMT-PDE Seminar (University of Minnesota), February 2021.

  • Euskal Herriko Unibertsitatea Analysis Seminar, November 2020.

  • University of Alabama Colloquium, January 2020.

  • SIAM Central States Section, October 2019.

  • University of Alabama Analysis Seminar, September 13, 2019.

  • University of Oregon Analysis Seminar, May 2019.

  • AMS Sectional Hartford, CT, April 2019.

  • University of Nebraska Colloquium, March 2019.

  • AMS Sectional: Nonlocal PDEs via Harmonic Analysis, SFSU, October 2018.

  • University of Connecticut Analysis Seminar, March 2018.

  • Harmonic Analysis in Winter, ICMAT, January 2018.

  • Rainwater Seminar, University of Washington, October 2017.

  • MSRI Postdoc Seminar, May 2017

  • AMS Sectional Meeting, Stony Brook University, March 2016.

  • University of Missouri Analysis Seminar, February 2016.

  • University of Minnesota PDE Seminar, November 2015.

  • University of Missouri Analysis Seminar, September, 2015.

  • Workshop in Harmonic Analysis, PDE, and Geometric Measure Theory, ICMAT-Madrid, January, 2015.

  • University of Missouri Analysis Seminar, November, 2014.