Zihui Zhao     pronounced as Zǐ-huì

Office:	Krieger 303
Email:	zhaozh [at] jhu [dot] edu

I am an Assistant Professor (tenure-track) at the Department of Mathematics of Johns Hopkins University, starting from 2023.

I was an NSF Postdoc and L.E. Dickson Instructor at the University of Chicago since August 2019. My mentor was Prof. Carlos Kenig.

From September 2018 to July 2019, I was a member at the Institute for Advanced Study during the Special 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, Harmonic Analysis, and PDEs.

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

If none of these jargons make any sense to you, here is a non technical explanation of my field of research!

A complete list of my preprints can also be viewed on my arXiv page.

• A Note on the Critical Set of Harmonic Functions Near the Boundary
  with Carlos Kenig
  Trans. Amer. Math. Soc.(2025) 378:3721-3754
• Elliptic Operators in Rough Sets, and the Dirichlet Problem with Boundary Data in Hölder Spaces
  with Mingming Cao, Pablo Hidalgo-Palencia, José María Martell, Cruz Prisuelos-Arribas
  J. Funct. Anal. (2025) 288 no. 5.
• Examples of non-Dini Domains with Large Singular Sets
  with Carlos Kenig
  Advanced Nonlinear Studies Special Issue: In honor of David Jerison (2023) 23 no. 1
• Expansion of Harmonic Functions Near the Boundary of Dini Domains
  with Carlos Kenig
  Rev. Mat. Iberoam. (2022) 38:2117-2152
• Elliptic Measures for Dahlberg-Kenig-Pipher Operators: Asymptotically Optimal Estimates
  with Simon Bortz, Tatiana Toro
  Math. Ann. (2023) 385:881-919
• Boundary Unique Continuation on Dini Domains and the Size of the Singular Set
  with Carlos Kenig
  Arch. Ration. Mech. An. (2022) 245:1-88
• Optimal Poisson Kernel Regularity for Elliptic Operators with Hölder-continuous Coefficients in Vanishing Chord-arc Domains
  with Simon Bortz, Tatiana Toro
  J. Funct. Anal. (2023) 285 no. 5.
• 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 of the series for publication) Geom. Funct. Anal. (2021) 31:325-401
• Two Phase Free Boundary Problem for Poisson Kernels
  with Simon Bortz, Max Engelstein, Max Goering, Tatiana Toro
  Indiana U. Math. J. (2022) 71:251-306
• Dirichlet Energy-minimizers with Analytic Boundary
  with Camillo De Lellis
  Indiana U. Math. J. (2023) 72:1367-1428
• 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

• Colloquium at Rice University, Mar. 2025
• Connections Workshop New Frontiers in Curvature & Special Geometric Structures and Analysis, SLMath Berkeley, Aug. 2024 video
• Calculus of Variations Workshop, Oberwolfach, Aug. 2024
• Geometry of Measures and Free Boundaries, a Conference in Honor of Tatiana Toro, University of Washington, Jul. 2024
• Geometric Measure Theory and Applications, Palazzone SNS, Cortona Italy, Jun. 2024
• Analysis Seminar, Brown University, Feb. 2024
• Geometry Seminar, Lehigh University, Feb. 2024
• Workshop on the Regularity Theory for Free Boundary and Geometric Variational Problems III, Levico Italy, Jun. 2023
• Analysis & PDE Seminar, Stanford University, May. 2023
• Workshop on Geometric Measure Theory and Harmonic Analysis, Hausdorff Research Institute for Mathematics, Apr. 2022 video
• MSRI Hot Topics Workshop Regularity Theory for Minimal Surfaces and Mean Curvature Flow, Mar. 2022 video
• Mini-course on Almgren's Regularity of Area-minimizing Currents and Multi-valued Functions, workshop on Geometric Measure Theory and Applications, University College London, Jul. 25-27, 2022
• Mini-course on the Quantitative Unique Continuation of Elliptic PDEs, workshop on the Free Boundary Problems and Related Topics, ETH Zurich, Jul. 4-8, 2022
• Minisymposium in Harmonic Analysis and PDE, 8th European Congress of Mathematics, Jun. 2021
• IAS Analysis Seminar, Institute for Advanced Study, Feb. 2019 video
• IAS Mathematical Conversations , IAS, Feb. 2019

• 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