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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Another mathematician Xiaolong (Hans) Han (韩肖垄)
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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.
A
list of my articles is available on arXiv
and MathSciNet
(authentication required).
Research
articles in chronological order:
•
Semiclassical measure of the spherical
harmonics by Bourgain on S3.
• Fractal
uncertainty principle for random Cantor sets, with P. Salekani.
• 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. Mathematical
Research Letters, 2023.
• 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 Notices, 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.
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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.
• Introduction to Probability.
• Applied Differential
Equations.
• Calculus III.
• Calculus I.
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Miscellany
notes:
• Develop a personal
teaching style.
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Editorial:
• I am an editor of Mathematics Exchange.
Please email me if you wish to submit a paper.
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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 340, Introduction to Probability and
Statistics.
• MATH 280, Applied
Differential Equations.
• MATH 250, Calculus
III.
• MATH 150A, Calculus
I.
• MATH 102, Pre-Calculus I.
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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.
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Collaborators:
• Michael Murray
• Chuong Tran
• Steve Zelditch
(1953-2022)