Long Jin
Long Jin
Associate Professor
Mathematical Science Center
Office: Shuangqing B525
Email: jinlong at mail.tsinghua.edu.cn
I work on analysis and partial differential equations, especially spectral and scattering theory, using tools from various fields, e.g. microlocal analysis.
Resonance-free region in scattering by a strictly convex obstacle, Arkiv för Matematik, 52 (2014), No.2, 257-289.
Scattering resonances of convex obstacles for general boundary conditions, Communications in Mathematical Physics, 335 (2015), No. 2, 759-807.
Semiclassical Cauchy estimates and applications, Transactions of the American Mathematical Society, 369 (2017), No. 2, 975-995.
(With Maciej Zworski) A local trace formula for Anosov flows, with appendices by Frédéric Naud, Annales Henri Poincaré, 18 (2017), No.1, 1-35. (A gap is fixed in a joint paper with Zhongkai Tao: arXiv:2204.02677)
(With Semyon Dyatlov) Resonances for open quantum maps and a fractal uncertainty principle, Communications in Mathematical Physics, 354 (2017), No. 1, 269-316.
(With Semyon Dyatlov) Dolgopyat's method and the fractal uncertainty principle, Analysis & PDE, 11 (2018), No. 6, 1457-1485.
(With Semyon Dyatlov) Semiclassical measures on hyperbolic surfaces have full support, Acta Mathematica, 220 (2018), No. 2, 297-339.
Control for Schrodinger equation on hyperbolic surfaces, Mathematical Research Letters, 25 (2018), No. 6, 1865-1877.
(With Ruixiang Zhang) Fractal uncertainty principle with explicit exponent, Mathematische Annalen, 376 (2020), No. 3-4, 1031-1057.
Damped wave equation on compact hyperbolic surfaces, Communications in Mathematical Physics, 373 (2020), No. 3, 771-794.
(With Kiril Datchev) Exponential lower resolvent bounds far away from trapped sets, Journal of Spectral Theory, 10 (2020), No. 2, 617-649.
(With Semyon Dyatlov and Stéphane Nonnenmacher) Control of eigenfunctions on surfaces of variable curvature, Journal of the American Mathematical Society, 35 (2022), No. 2, 361-465.
(With Zhongkai Tao) Flat trace estimates for Anosov flows, Mathematical Research Letters, 32 (2025), No. 2, 415-426.
(With Zhongkai Tao) Counting Pollicott-Ruelle resonances for Axiom A flows, Communications in Mathematical Physics, 406 (2025) Paper No. 26
(With Yulin Gong) Sublinear lower bounds of eigenvalues for twisted Laplacian on compact hyperbolic surfaces, to appear in Peking Mathematical Journal, arXiv:2504.12666
(With An Zhang and Hong Zhang) Quantitative FUP and spectral gap for quasi-Fuchsian group, preprint, arXiv:2601.19663
(With An Zhang and Hong Zhang) Anisotropic 2D FUP and quantum open baker's map, preprint, arXiv:2606.23160
Summer 2013: Math 54, Linear Algebra and Differential Equations, UC Berkeley,
Fall 2016-Spring 2018: Math 266, Ordinary Differential Equations, Purdue University.
Spring 2019/2020: Measure and Integration. 测度与积分
Fall 2019/2022, Semiclassical and Microlocal analysis. 半经典与微局部分析
Fall 2020, Analysis of Linear Differential Operators. 线性微分算子分析
Spring 2021, Topics on Applied Partial Differential Equations, (Control theory of PDE, joint with Jing Wenjia.）应用偏微分方程选讲，与荆文甲合讲
Fall 2021-Spring 2022, Analysis I&II. 分析1&2
Spring 2023/2025, Partial Differential Equations II. 偏微分方程II (joing with Wang Xuecheng in 2025)
Fall 2023/2024/2025, Ordinary Differential Equations and Dynamical Systems. 常微分方程与动力系统
Spring 2024, Topics in Dynamical Systems. 动力系统专题（双曲动力系统的微局部分析方法，zeta函数，Pollicott-Ruelle共振谱与其它）
I am coorganizing Seminar on Microlocal Analysis and Applications with Chen Xi (Fudan University)
我与复旦大学陈曦联合组织线上微局部分析以及应用讨论班。
Scattering Resonances for Convex Obstacles, PhD Thesis, UC Berkeley
Quantum chaos and fractal uncertainty principle, Proceedings of the International Consortium of Chinese Mathematicians 2018, International Press, Boston, MA, 2020, 293–309.