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I am Zhongkai Tao. I am a junior professor at the Institut des Hautes Études Scientifiques (IHES). I am interested in analysis, especially spectral and microlocal/harmonic analysis methods in partial differential equations, dynamical systems, and condensed matter physics.
I was a graduate student at the University of California, Berkeley, supervised by Maciej Zworski.
My email is ztao@ihes.fr. Here is my CV.
My research:
Spectral theory, scattering resonances, and uncertainty principle:
Lossless Strichartz and spectral projection estimates on unbounded manifolds, with Xiaoqi Huang, Christopher Sogge and Zhexing Zhang.
Selberg, Ihara and Berkovich, with Jialun Li, Carlos Matheus and Wenyu Pan.
Spectral gap for surfaces of infinite volume with negative curvature.
Optimal enhanced dissipation for contact Anosov flows, with Maciej Zworski, Nonlinearity, 38(2025), no.4, 045001.
Counting Pollicott--Ruelle resonances for Axiom A flows, with Long Jin, Communications in Mathematical Physics, 406 (2025), No. 26.
The fractal uncertainty principle via Dolgopyat's method in higher dimensions, with Aidan Backus and James Leng, Analysis and PDE, 18 (2025), No. 7, 1769–1804.
Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds, with Qiuyu Ren, to appear in Mathematische Annalen.
Spectral asymptotics for kinetic Brownian motion on locally symmetric spaces, with Qiuyu Ren.
Flat trace estimates for Anosov flows, with Long Jin, Mathematical Research Letters, 32(2) (2025), pp. 415–426.
Exact control for Schrödinger equation on torus from small balls, Pure and Applied Analysis 3 (2021), 387–401.
On 0-th order pseudodifferential operator on the circle, Proceedings of the AMS, 152 (2024), no.8, 3289–3297.
Underdetermined PDE systems and general relativity:
Flexibility of maximal asymptotically flat initial data sets, with Yuchen Mao and Sung-Jin Oh, in preparation;
Integral formulas for under/overdetermined differential operators via recovery on curves and the finite-dimensional cokernel condition I: General theory, with Philip Isett, Yuchen Mao and Sung-Jin Oh.
Initial data gluing in the asymptotically flat regime via solution operators with prescribed support properties, with Yuchen Mao and Sung-Jin Oh.
Localized initial data for Einstein equations, with Yuchen Mao.
Condensed matter physics:
Wannier decay and the Thouless conjecture, with Simon Becker and Mengxuan Yang.
Fragile topology on solid grounds: a mathematical perspective, with Simon Becker and Mengxuan Yang.
Dirac cones and magic angles in the Bistritzer--MacDonald TBG Hamiltonian, with Simon Becker, Solomon Quinn, Alexander Watson and Mengxuan Yang.
Appendix to Mathematical results on the chiral model of twisted bilayer graphene, with Mengxuan Yang, Journal of Spectral Theory, 14 (2024), no.3, 1063–1107.
Appendix to Classically forbidden regions in the chiral model of twisted bilayer graphene, with Maciej Zworski, Probability and Mathematical Physics, 6 (2025), No. 2, 505–546.
Notes:
Notes on random perturbation of non-self-adjoint operators, taken from the topics course in Spring 2021 taught by Maciej Zworski.
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