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I am currently a postdoc at the Department of Mathematics at MIT, hosted by David Jerison.
Between 2020-2022 I was a postdoc member at the IAS, hosted by Peter Sarnak.
I completed my Ph.D. at the Technion, under the supervision of Ram Band.
My field of research is mathematical physics.
Topics of Interest:
Quantum graphs
Quantum chaos
Spectral geometry and nodal count
Quasi-Crystals
Related fields:
Graph theory
Probability
Dynamics and ergodic theory
Fourier analysis
Real algebraic geometry
Contact
Research
Video
Publications
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
Nodal statistics on quantum graphs
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
Neumann domains on quantum graphs
L Alon, R Band (2021)
Annals of Henri Poincare,22, 3391 - 3454. arXiv 1911.12435
Universality of nodal count distribution in large metric graphs
L Alon, R Band, G Berkolaiko (2022)
Experimental Mathematics,1-35. arXiv 2106.06096
Accepted
Generic Laplace eigenfunctions on metric graphs
L Alon
Accepted to Journal d'Analyse Mathématique.
Morse theory for discrete magnetic operators and nodal count distribution for graphs
L Alon, M Goresky
Accepted to Journal of Spectral Theory
Preprints
Every real-rooted exponential polynomial is the restriction of a Lee-Yang polynomial
L Alon, A Cohen, and C Vinzant.
arXiv:2303.03201
Ph.D. thesis
Quantum graphs - Generic eigenfunctions and their nodal count and Neumann count statistics
L Alon
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.
Berry phase
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.
Related Images
By clicking on each image you can see its description and a link to the relevant poster
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Contact
MIT- Massachusetts Institute of Technology
77 Massachusetts Ave, Cambridge, MA 02139-4307
USA
Mathematics department, Room 241
Home Address: 1 Dana street, apartment 20, Cambridge, MA 02138
Email: lioralon@mit.edu
Secondary Email: