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:
•
Small scale
quantum ergodicity in cat
maps. I.
•
Spherical
harmonics and point configurations on the sphere. To appear in Geometric
and Functional Analysis.
•
Fractal
uncertainty principle for random Cantor sets, with P. Salekani.
To appear in Journal of the Australian Mathematical Society.
•
The
semiclassical measure of certain spherical harmonics on
S3.
To appear in
Indiana University
Mathematics Journal.
•
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)