Zihui Zhao     pronounced as Zǐ-huì

Office:	Simonyi Hall 219
Email:	zzhao [at] ias [dot] edu

Since August 2019, I am an NSF Postdoc and L.E. Dickson Instructor at the University of Chicago.

From September 2018 to July 2019, I was a member at the Institute for Advanced Study during the Sepcial Year on Variational Methods in Geometry . My mentor was Prof. Camillo De Lellis .

In June 2018 I graduated from the University of Washington, and my advisor was Prof. Tatiana Toro.

You can find my CV here .

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.

• Uniform Rectifiability and Elliptic Operators Satisfying a Carleson Measure Condition. Part II: The Large Constant Case
  with Steve Hofmann, José María Martell, Svitlana Mayboroda, Tatiana Toro
  Submitted on arXiv
• Two Phase Free Boundary Problem for Poisson Kernels
  with Simon Bortz, Max Engelstein, Max Goering, Tatiana Toro
  Submitted on arXiv
• Dirichlet Energy-minimizers with Analytic Boundary
  with Camillo De Lellis
  Submitted on arXiv
• Dirichlet Problem in Domains with Lower Dimensional Boundaries
  with Joseph Feneuil, Svitlana Mayboroda
  Submitted on arXiv
• Square Function Estimates, BMO Dirichlet Problem, and Absolute Continuity of Harmonic Measure on Lower-dimensional Sets
  with Svitlana Mayboroda
  Anal. PDE (2019) 12:1843-1890
• Uniform Rectifiability and Elliptic Operators Satisfying a Carleson Measure Condition. Part I: The Small Constant Case
  with Steve Hofmann, José María Martell, Svitlana Mayboroda, Tatiana Toro
  Submitted on arXiv
• Boundary Rectifiability and Elliptic Operators with W^{1,1} Coefficients
  with Tatiana Toro
  To appear on 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

• Harmonic Analysis and PDEs , University of Helsinki, Jun. 3-7, 2019
• AMS Sectional Meeting
  Special Session on Topics at the Interface of Analysis and Geometry
  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

• In the 2019 Women and Mathematics Program: Topics in Geometric Analysis , I held the review sessions alongside the Terng Lectures given by Prof. Tatiana Toro, May 18-24, 2019.
• 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