Research
Papers and preprints:
1) "Cantor sets with absolutely continuous harmonic measure." With Guy David and Antoine Julia. J. Ec. Polytech. Math. 10, (2023).
2) "Non-local distance functions and geometric regularity." With Max Engelstein and Svitlana Mayboroda, accepted for publication in Adv. Math.
3) "Small-constant uniform rectifiability." J. Geom. Anal. 34, 125 (2024).
4) "On the number of nodal domains of homogeneous caloric polynomials." With Matthew Badger. Submitted for publication.
In preparation:
5) "Small A-infinity results for Dahlerberg-Kenig-Pipher operators outside of low-dimensional, uniformly rectifiable sets." With Max Engelstein, Linhan Li, and Svitlana Mayboroda. In preparation.
Scientific posters and talks (slides, and some videos, some notes):
On the number of nodal domains of homogeneous caloric polynomials. Online talk given in the Simons Collaboration on Wave Localization geometric measure theory subgroup, January 2023.
Non-local distances and geometric regularity of measures. Talk given at the AMS Special Session in recent developments in geometric measure theory, JMM in Boston January 2023.
Small A_\infty results for elliptic measure outside of low-dimensional, small constant, uniformly rectifiable sets. Talk given at the harmonic functions and Laplace eigenfunctions special session at the PRIMA 2022 Conference in Vancouver, December 2022.
Non-local distances and geometric regularity of measures. Talk given in the UConn PDE seminar, November 2022.
Large-scale regularity theory for elliptic systems in stochastic homogenization. An expository talk on the paper of Neukamm, Otto, and Gloria here, given at the 2022 Oberwolfach Arbeitsgemeinschaft in quantitative stochastic homogenization. I also organized the report of the Arbeitsgemeinschaft.
Non-local distances and geometric regularity of measures. Talk given at the UAB Analysis seminar, in Barcelona, October 2022.
On the fundamental solution of generalized Schrodinger operators. An expository talk on Z. Shen's paper here, given at the 2022 Bonn summer school in nodal domains organized by the HCM. Given in Kopp, Germany, October 2022.
Non-local distances and geometric regularity of measures. Talk given at the UMN PDE seminar, in Minneapolis MN, September 2022.
Non-local distances and geometric regularity of measures. Scientific poster presented at the 2022 Simons Localization of Waves annual meeting.
Regularized distances and measures. An online talk given at the Kansas Prairie Analysis Seminar, November 2021.
Regularized Distance Kernels. An online talk given in the UMN Harmonic Analysis, GMT, PDE seminar in Spring 2021.