Zihui Zhao     pronounced as Zǐ-huì

Office:	Ryerson 351
Email:	zhaozh [at] uchicago [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 Measure Theory, Geometric Analysis, PDEs and Harmonic Analysis.

In particular I am interested in regularity problems of minimal surfaces and area-minimizing currents; unique continuation problems; the properties of the harmonic and elliptic measures and their relations to elliptic boundary value problem.

• Elliptic Measures for Dahlberg-Kenig-Pipher Operators: Asymptotically Optimal Estimates
  with Simon Bortz, Tatiana Toro
  Submitted on arXiv
• Boundary Unique Continuation on Dini Domains and the Size of the Singular Set
  with Carlos Kenig
  Submitted on arXiv
• Optimal Poisson Kernel Regularity for Elliptic Operators with Hölder-continuous Coefficients in Vanishing Chord-arc Domains
  with Simon Bortz, Tatiana Toro
  Submitted on arXiv
• 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
  Combined with Part I and to appear on Geom. Funct. Anal.
• Two Phase Free Boundary Problem for Poisson Kernels
  with Simon Bortz, Max Engelstein, Max Goering, Tatiana Toro
  To appear on Indiana U. Math. J.
• 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
  Rev. Mat. Iberoam. (2021) 37:821-910
• 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
  Adv. Calc. Var. (2021) 14:37-62
• BMO Solvability and the A-infty Condition of the Elliptic Measure in Uniform Domains
  J. Geom. Anal. (2018) 28:866-908

• Analysis & PDE Seminar, Stanford University, May. 2021
• Geometric Analysis Seminar, University of California San Diego, Apr. 2021
• PDE Seminar, University of Minnesota, Mar. 2021
• Rainwater Seminar, University of Washington, Dec. 2020
• Virtual Maxwell Analysis Seminar, University of Edinburgh and Heriot-Watt University, Oct. 2020
• Mid-Atlantic Analysis Meeting Seminar, Sep. 2020
• Oberwolfach Workshop on Calculus of Variations, Aug. 2-8, 2020
• PDE CDT Lunchtime Seminar, University of Oxford, May. 2020
• PDE Seminar, Purdue University, Jan. 2020
• Calderón-Zygmund Analysis Seminar, University of Chicago, Nov. 2019
• 2019 Prairie Analysis Seminar, Kansas State University, Nov. 8-9, 2019
• Harmonic Analysis and PDEs conference , 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. 2019
• IAS Mathematical Conversations , IAS, Feb. 2019
• Princeton/IAS GMT Seminar , Princeton University, Dec. 2018
• Analysis Seminar , University of Pennsylvania, Nov. 2018
• Harmonic Analysis and PDE Seminar , CUNY Graduate Center, Sep. 2018
• PCMI Research Program, PCMI , Jul. 2018
• Analysis and Applications Seminar , ICMAT, Madrid, Sep. 2017

• I co-organized the AMS special session on Interfaces between PDEs and geometric measure theory together with Robin Neumayer at the Joint Mathematics Meetings in Denver, Jan. 15-18, 2020.
• 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.
• I co-organized the AMS special session on Regularity theory of PDEs and calculus of variations on domains with rough boundaries together with Murat Akman at the University of Connecticut, Apr. 13-14, 2019.

• Autumn 2020 - Math 16110/50: Honors Calculus I (Inquiry-Based Learning)
• Summer 2018 - Math 307F: Introduction to Differential Equations