Office: | Simonyi Hall 219 |

Email: | zzhao [at] ias [dot] edu |

I am a member at the Institute for Advanced Study during the Sepcial Year on Variational Methods in Geometry. My mentor is Prof. Camillo De Lellis. In June 2018 I graduated from the University of Washington, and my advisor was Prof. Tatiana Toro.

Starting from August 2019, I will be a Dickson Instructor and NSF Postdoc at the University of Chicago.

Broadly speaking my work lies in the intersection of geometric analysis, geometric measure theory, harmonic analysis and PDEs.

In particular I am interested in the properties of the harmonic and elliptic measure, how they are related to the geometric characterization of the domain considered and the boundary behavior of solutions to elliptic PDEs. I am also interested in regularity problems of minimal surfaces.

- Dirichlet problem in domains with lower dimensional boundaries

submitted on arXiv:1810.06805 - Square function estimates, BMO Dirichlet problem, and absolute continuity of harmonic measure on lower-dimensional sets

to appear in Anal. PDE 2018 - Uniform rectifiability and elliptic operators with small Carleson norm

submitted on arXiv:1710.06157 - Boundary rectifiability and elliptic operators with W^{1,1} coefficients

to appear in Adv. Calc. Var. 2017 - BMO solvability and the A-infty condition of the elliptic measure in uniform domains

J. Geom. Anal. (2018) 28:866-908

- AMS Sectional Meeting, Special Session on Topics at the Interface of Analysis and Geometry and Special Session on Interactions between Geometric Measure Theory, PDE, and Harmonic Analysis, University of Hawaii at Manoa, Mar. 22-24, 2019
- IAS Analysis Seminar, IAS, Feb. 14, 2019
- IAS Mathematical Conversations, IAS, Feb. 13, 2019
- Princeton/IAS GMT Seminar, Princeton University, Dec. 5 2018
- Analysis Seminar, University of Pennsylvania, Nov. 1, 2018
- Harmonic Analysis and PDE Seminar, CUNY Graduate Center, Sep. 14, 2018
- PCMI Research Program, PCMI, Jul. 13, 2018
- Rainwater Seminar, University of Washington, May. 1, 2018
- AMS Sectional Meeting, Northeastern University, Apr. 21-22, 2018
- Analysis and Applications Seminar, ICMAT, Sep. 19, 2017
- S.I.G.M.A. Seminar, University of Connecticut, Jun. 16, 2017
- Harmonic Analysis and Differential Equations Student Seminar, University of California, Berkeley, Mar. 21, 2017
- Graduate Student Seminar, MSRI, Mar. 1, 2017
- AMS Sectional Meeting, Bowdoin College, Sep. 24, 2016

- Together with Murat Akman, I co-organized the AMS Special Session on
*Regularity Theory of PDEs and Calculus of Variations on Domains with Rough Boundaries*at the University of Connecticut, Apr. 13-14, 2019.

- Summer 2018 - Math 307F: Introduction to Differential Equations