I am an RTG Postdoctoral Fellow at Northwestern University under the mentorship of Steve Zelditch.
Ph.D. Advisor: Chris Sogge
Ph.D. in Mathematics
Johns Hopkins Univerisity
Conferred May, 2018
B.A. in Mathematics with Highest Honors
University of Rochester
Conferred May, 2013
Link to my CV (current as of April, 2021)anchor
I use tools of microlocal analysis to study the asymptotic distribution of Laplace eigenfunctions over manifolds, and how these asymptotics respond to the geometry of the manifold and dynamics of the geodesic flow. This field finds relevance to a wide range of disciplines, from quantum physics to number theory. My recent interests include Fourier coefficients of eigenfunctions restricted to curves, asymptotics on product manifolds, and some similar joint spectral asymptotic problems.
I've recently been interested in problems related to measures in Euclidean space which admit a basis or frame of Fourier exponentials. In particular, I am working to translate some of these results (e.g. Weyl laws, Beurling densities, Fuglede's conjecture) to the Riemannian setting. That is, to regions in manifolds which admit a basis or frame of Laplace eigenfunctions.anchor
Postdoctoral Teaching ExperienceCourses Taught at Northwestern University:
- Math 230-2: Multivariable Integral Calculus. Spring 2021
- Math 218-3: Single Variable Calculus with Precalculus. Fall 2020
- Math 334: A Second Course in Linear Algebra. Spring 2020
- Math 234: Multiple Integration and Vector Calculus. Fall 2019
- Math 230: Differential Calculus of Multivariable Functions. Winter 2019
- Math 220: Differential Calculus of One Variable Functions. Fall 2018
TA for Eigenfunctions minicourse for SNAP at Northwestern University, summer 2019.
A three-week summer mathematics program aimed at an audience ranging from advanced undergraduates to recent Ph.D.s, featuring minicourses and talks on Fourier analysis, semiclassical analysis, eigenfunctions, and scattering theory. (Program website)
Co-instructor for the STEMForAll summer program at the University of Rochester, summer 2019.
A four-week summer program for undergraduate students on a variety of topics with minicourse and research components, with an emphasis on involving students from traditionally under-represented groups in cutting edge mathematics. (Program website) (My lecture notes)
Co-organizer for the NSF Tripods REU/STEMForAll summer program at the University of Rochester, summer 2020.
A two-week summer mathematics program for undergraduate students on high-dimensional probability and data science with minicourse and Python programming components, with an emphasis on involving students from traditionally under-represented groups in cutting edge mathematics. (Program website) (Program poster)anchor
Awards & Honors
Professor Joel Dean Award for extraordinary performance in undergraduate teaching. Johns Hopkins University, 2017.
The Owen Award for outstanding qualifications upon admittance to Johns Hopkins University, 2013.
Arthur S. Gale Memorial Prize for the highest performing graduating senior in mathematics. The University of Rochester, 2013.anchor
- Analysis and PDE Seminar at Stanford University, 2021 (Slides)
- Analysis Seminar at the University of Rochester, 2018 (Slides)
- Tianyuan Advanced Seminar on Harmonic Analysis, Geometry, and PDEs, 2018 (Slides)
- Mathematics Colloquium at Georgetown University, 2017
- Global Harmonic Analysis AMS Special Session, 2017
Publications and Preprints
- Triangles and triple products of Laplace eigenfunctions. arXiv:2103.03336, 2021.
- Fourier coefficients of restrictions of eigenfunctions with Yakun Xi and Steve Zelditch. arXiv:2011.11571, 2020.
- Improved Weyl remainder for products of spheres with Alex Iosevich. To appear in Analysis Mathematica, 2019.
- Fourier frames for surface-carried measures with Alex Iosevich, Chun-Kit Lai, and Bochen Liu. To appear in International Mathematics Research Notices, 2020.
- Improved generalized period estimates over curves on Riemannian surfaces with nonpositive curvature with Yakun Xi. arXiv:1807.00041, 2018.
- Period integrals in nonpositively curved manifolds. Mathematical Research Letters, 2019.
- Looping directions and integrals of eigenfunctions over submanifolds. Journal of Geometric Analysis, 2018.
- Explicit bounds on integrals of eigenfunctions over curves in surfaces of nonpositive curvature. Journal of Geometric Analysis, 2018.
- Integrals of eigenfunctions over curves in surfaces of nonpositive curvature. arXiv:1702.03552, 2017.