Previously, I held a postdoc position at IAS (Princeton) from 2020 to 2022, hosted by Peter Sarnak, following the completion of my Ph.D. in mathematics at the Technion in 2020, where I had the pleasure of being advised by Ram Band.
My research lies within mathematical physics, and intersects with various mathematical disciplines, including Spectral Geometry, Graph Theory, Morse Theory, Real Algebraic Geometry, Fourier Analysis, Dynamics, and Number Theory.
Here are some of my recent works:
Generic Laplace eigenfunctions on metric graphs
A detailed list of publications is found below, as well as nice pictures from these works and other projects.
L Alon, A Cohen, and C Vinzant (2023)
Journal of Functional Analysis, Volume 286, Issue 2, 2024, doi: 10.1016/j.jfa.2023.110226.
L Alon (2023)
Journal d'Analyse Mathématique. doi: 10.1007/s11854-023-0308-x
L Alon, R Band, G Berkolaiko (2022)
Experimental Mathematics,1-35. arXiv 2106.06096
L Alon, R Band (2021)
Annals of Henri Poincare,22, 3391 - 3454. arXiv 1911.12435
Neumann domains on graphs and manifolds
L Alon, R Band, M Bersudsky, S Egger (2020)
Analysis and Geometry on Graphs and Manifolds 461, 203. arXiv 1805.07612
L Alon, R Band, G Berkolaiko (2017)
Communications in Mathematical Physics 362 (3), 909-948. arXiv 1709.10413
Cerenkov radiation from particles carrying orbital angular momentum in a cylindrical waveguide
Y Shapira, M Mutzafi, G Harari, I Kaminer, L Alon, M Segev (2016)
Conference on Lasers and Electro-Optics (CLEO), 1-2
L Alon, M Goresky
To appear in Journal of Spectral Theory
Gap distributions of Fourier quasicrystals via Lee-Yang polynomials
L Alon, A Cohen, and C Vinzant.
Quantum graphs - Generic eigenfunctions and their nodal count and Neumann count statistics
This gif shows the evolution of a wave function on a quantum graph.
In this plot we see |f(x,t)|^2 (the probability density) changing in time according to Schrödinger's equation, starting from a Gaussian of positive velocity.
How a continuous periodic change of edge lengths can "flip" an eigenfunction.
Left: closed path in the parameter space - possible edge lengths (L1,L2,L3) for which the star graph has eigenvalue equal to 1.
Right: The corresponding eigenfunction of eigenvalue 1, changing continuously with the edge lengths.
TEACHING (T.A) NOTES
בלינק הבא תמצאו את התירגולים שלי בחדוא 2ת. תירגלתי את הקורס בשנים 2015-2019
You can find my tutorial notes in the following link. These are in Hebrew