Xiaolong Han (韩晓龙)

Department of Mathematics

California State University, Northridge (CSUN)

Northridge, CA 91330, USA

Phone: 1 # 818 # 677 # 2710

Email: xiaolong.han at csun.edu

-----------------------------------------------------------------------------------------------------------

Another mathematician Xiaolong (Hans) Han (韩肖垄)

-----------------------------------------------------------------------------------------------------------

Here is my CV.

-----------------------------------------------------------------------------------------------------------

Research interests: Microlocal and semiclassical analysis, harmonic analysis, spectral and scattering theory, quantum chaos.

Article lists are available in arXiv and in MathSciNet (authentication required).

Research articles in chronological order:

      Fractal uncertainty principle for random Cantor sets, with P. Salekani.

      Uniformly bounded spherical harmonics and quantum ergodicity.

      Small scale quantum ergodicity in cat maps. II. Quasimodes that are not equidistributed at the logarithmical scales.

      Small scale quantum ergodicity in cat maps. I.

      Fractal uncertainty principle for discrete Cantor sets with random alphabets, with S. Eswarathasan. To appear in Mathematical Research Letters.

      Riemann moduli spaces are quantum ergodic, with D. Baskin and J. Gell-Redman. Journal of Differential Geometry, 2023.

      From nodal points to non-equidistribution at the Planck scale. Comptes Rendus Mathématique, 2022.

      Tomas-Stein restriction estimates on convex cocompact hyperbolic manifolds, International Mathematics Research Notice, 2021.

      Equidistribution of random waves on small balls, with M. Tacy. Communications in Mathematical Physics, 2020.

      Nodal lengths of eigenfunctions in the disc, with M. Murray and C. Tran. Proceedings of the American Mathematical Society, 2019.

      Lp bilinear quasimode estimates, with Z. Guo and M. Tacy. Journal of Geometric Analysis, 2019.

      Distribution of the nodal sets of eigenfunctions on analytic manifolds. Journal of Spectral Theory, 2018.

      Small scale equidistribution of random eigenbases. Communications in Mathematical Physics, 2017.

      Spherical harmonics with maximal Lp (2<p<=6) norm growth. Journal of Geometric Analysis, 2016.

      Small scale quantum ergodicity in negatively curved manifolds. Nonlinearity, 2015.

      Sharp norm estimates of layer potentials and operators at high energy, with M. Tacy and an appendix by J. Galkowski. Journal of Functional Analysis, 2015.

      Completeness of boundary traces of eigenfunctions, with A. Hassell, H. Hezari, and S. Zelditch. Proceedings of the London Mathematical Society, 2015.

      Existence of maximizers for Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. Indiana University Mathematics Journal, 2013.

      Hardy-Littlewood-Sobolev and Stein-Weiss inequalities and integral systems on the Heisenberg group, with G. Lu and J. Zhu. Nonlinear Analysis, 2012.

      On regularity of solutions to an integral system associated with Bessel potentials, with G. Lu. International Journal of Mathematics, 2012.

      Dual spaces of weighted multi-parameter Hardy spaces associated with the Zygmund dilation, with G. Lu and Y. Xiao. Advanced Nonlinear Studies, 2012.

      Characterization of balls in terms of Bessel-potential integral equation, with G. Lu and J. Zhu. Journal of Differential Equations, 2012.

      Regularity of solutions to an integral equation associated with Bessel potential, with G. Lu. Communications on Pure Applied Analysis, 2011.

      A geometric covering lemma and nodal sets of eigenfunctions, with G. Lu. Mathematical Research Letters, 2011.

-----------------------------------------------------------------------------------------------------------

Seminar notes:

      Problems.

      Harmonic functions and nodal sets by Logunov-Malinnikova.

      Dynamical zeta functions for Anosov systems via microlocal analysis by Dyatlov-Zworski.

      Classical ergodicity.

      Intersecting Lagrangian distributions by Melrose-Uhlmann.

      Fourier integral operators by Duistermaat-Hörmander.

-----------------------------------------------------------------------------------------------------------

Lecture notes:

      Complex Analysis.

      Real Analysis.

      Topology.

      Mathematical Analysis.

      Differential Equations.

      Introduction to Probability.

      Applied Differential Equations.

      Calculus III.

      Calculus I.

-----------------------------------------------------------------------------------------------------------

Miscellany notes:

      Develop a (personal) teaching style.

-----------------------------------------------------------------------------------------------------------

Editorial:

      I am an editor of Mathematics Exchange. To submit a paper, you can email it to me.

-----------------------------------------------------------------------------------------------------------

Courses taught at CSUN:

      MATH 655, Complex Analysis.

      MATH 651A, Advanced Topic in Analysis: Harmonic Functions and Nodal Sets.

      MATH 552, Real Analysis.

      MATH 550, Calculus on Manifolds.

      MATH 501, Topology.

      MATH 450B, Advanced Calculus II.

      MATH 450A, Advanced Calculus I.

      MATH 351, Differential Equations.

      MATH 340, Introduction to Probability and Statistics.

      MATH 280, Applied Differential Equations.

      MATH 250, Calculus III.

      MATH 150A, Calculus I.

      MATH 102, Pre-Calculus I.

-----------------------------------------------------------------------------------------------------------

Students supervised at CSUN:

      2023 Fall, K. Jannati, M.S. in Mathematics. Thesis: A fractal uncertainty principle of discrete Fourier transform on Cantor sets.

      2022 Fall, K. Schmidt, M.S. in Mathematics. Thesis: Dvir’s solution to the Kakeya conjecture in finite fields.

      2022 Spring, J. Horowitz, M.S. in Mathematics. Thesis: Hyperbolic toral automorphisms: A case study of mathematical chaos.

      2020 Fall, D. Nolasco, M.S. in Mathematics. Thesis: Riemann zeta function and the prime number theorem.

      2020 Spring, A. Britton, M.S. in Mathematics. Thesis: Harmonic functions and nodal sets.

      2019 Spring, M. Murray, M.S. in Mathematics. Thesis: Nodal lengths of eigenfunctions in the disc.

-----------------------------------------------------------------------------------------------------------

Collaborators:

      Dean Baskin

      Suresh Eswarathasan

      Jeff Galkowski

      Jesse Gell-Redman

      Zihua Guo

      Andrew Hassell

      Hamid Hezari

      Guozhen Lu

      Michael Murray

      Pouria Salekani

      Melissa Tacy

      Chuong Tran

      Yayuan Xiao

      Steve Zelditch (1953-2022)

      Jiuyi Zhu