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.