Xiaolong
Han (韩晓龙)
California State University, Northridge (CSUN)
Northridge,
CA 91330, USA
Phone:
1 # 818 # 677 # 2710
Email:
xiaolong.han at csun.edu
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Here
is my CV.
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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:
• Uniformly
bounded spherical harmonics and quantum ergodicity.
• 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 123 (2023), no. 3, 391-410.
• From
nodal points to non-equidistribution at the Planck
scale. Comptes Rendus Mathématique 360 (2022), 451-458.
• Tomas-Stein restriction estimates on
convex cocompact hyperbolic manifolds,
International
Mathematics Research Notice (2021), no. 11, 8337-8352.
• Equidistribution
of random waves on small balls,
with M. Tacy. Communications
in Mathematical Physics 376 (2020), no. 3, 2351-2377.
• Nodal lengths of eigenfunctions in the
disc, with M. Murray and C. Tran. Proceedings
of the American Mathematical Society 147 (2019), no. 4, 1817-1824.
• Lp bilinear quasimode estimates,
with Z. Guo and M. Tacy. Journal of Geometric
Analysis 29 (2019), no. 3, 2242-2289.
• Distribution of the nodal sets of
eigenfunctions on analytic manifolds. Journal
of Spectral Theory 8 (2018), no. 4, 1281-1293.
• Small scale equidistribution
of random eigenbases. Communications
in Mathematical Physics 349 (2017), no. 1, 425-440.
• Spherical harmonics with maximal Lp (2<p<=6) norm growth. Journal of
Geometric Analysis 26 (2016), no. 1, 378-398.
• Small scale quantum ergodicity in
negatively curved manifolds. Nonlinearity
28 (2015), no. 9, 3262-3288.
• Sharp norm estimates of layer potentials
and operators at high energy, with M. Tacy and an appendix by J. Galkowski. Journal
of Functional Analysis 269 (2015), no. 9, 2890-2926.
• Completeness of boundary traces of
eigenfunctions, with
A. Hassell, H. Hezari, and S. Zelditch.
Proceedings of the
London Mathematical Society (3) 111 (2015), no. 3, 749-773.
• Existence of maximizers for
Hardy-Littlewood-Sobolev inequalities on the
Heisenberg group. Indiana
University Mathematics Journal 62 (2013), no. 3, 737-751.
• Hardy-Littlewood-Sobolev and Stein-Weiss inequalities and integral systems
on the Heisenberg group,
with G. Lu and J. Zhu. Nonlinear
Analysis 75 (2012), no. 11, 4296-4314.
• On
regularity of solutions to an integral system associated with Bessel potentials, with G. Lu. International
Journal of Mathematics 23 (2012), no. 5, 1250051.
• Dual
spaces of weighted multi-parameter Hardy spaces associated with the Zygmund dilation, with G. Lu and Y. Xiao. Advanced
Nonlinear Studies 12 (2012), no. 3, 533-553.
• Characterization
of balls in terms of Bessel-potential integral equation, with G. Lu and J. Zhu. Journal
of Differential Equations 252 (2012), no. 2, 1589-1602.
• Regularity
of solutions to an integral equation associated with Bessel potential, with G. Lu. Communications
on Pure Applied Analysis 10 (2011), no. 4, 1111-1119.
• A
geometric covering lemma and nodal sets of eigenfunctions, with G. Lu. Mathematical
Research Letters 18 (2011), no. 2, 337-352.
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Seminar
notes:
• Problems.
• Harmonic functions and nodal
sets by Logunov-Malinnikova.
• Dynamical zeta functions for Anosov systems via microlocal analysis by Dyatlov-Zworski.
• Intersecting
Lagrangian distributions by Melrose-Uhlmann.
• Fourier integral operators by Duistermaat-Hörmander.
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Lecture
notes:
• Topology.
• Applied Differential Equations.
• Calculus III.
• Calculus I.
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Miscellany
notes:
• Develop a (personal)
teaching style.
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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 280, Applied
Differential Equations.
• MATH 250, Calculus
III.
• MATH 150A, Calculus
I.
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Students supervised at CSUN:
• 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.
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Collaborators:
• Michael Murray
• Chuong Tran
• Steve Zelditch
(1953-2022)
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Another mathematician Xiaolong (Hans) Han (韩肖垄).