I am a postdoc at MIT, hosted by David Jerison. Between 2020-2022 I was a postdoc at the IAS, hosted by Peter Sarnak. I did my Ph.D. in the Technion, with Ram Band as my advisor. My field of research is mathematical physics.
Topics of Interest:
Spectral geometry and nodal count
Dynamics and ergodic theory
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, R Band, G Berkolaiko (2017)
Communications in Mathematical Physics 362 (3), 909-948. arXiv 1709.10413
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 (2021)
Annals of Henri Poincare,22, 3391 - 3454. arXiv 1911.12435
L Alon, R Band, G Berkolaiko (2022)
Experimental Mathematics,1-35. arXiv 2106.06096
Generic Laplace eigenfunctions on metric graphs
Accepted to Journal d'Analyse Mathématique.
Quantum graphs - Generic eigenfunctions and their nodal count and Neumann count statistics
A Quantum Graph
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