Lior_Alon_profile_picture.jpg

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:

  • Quantum graphs

  • Quantum chaos

  • Spectral geometry and nodal count

  • Quasi-Crystals

Related fields:

  • Graph theory

  • Probability

  • Dynamics and ergodic theory

  • Fourier analysis

Contact

lioralon@mit.edu

 

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

arXiv 2203.16111

Accepted to Journal d'Analyse Mathématique. 

Ph.D. thesis

Quantum graphs - Generic eigenfunctions and their nodal count and Neumann count statistics

L Alon

arXiv 2010.03004

 

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.

ezgif.com-gif-maker.gif
 

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. 

Berryphase.gif
 

Related Images

By clicking on each image you can see its description and a link to the relevant poster

Secular manifold
XxT.jpg
secular manifold
secular manifold
An eigenfunction on a graph
 

Teaching (T.A) Notes

Calculus 2

חדו"א 2ת

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

Complex Analysis

תורת הפונקציות (פונקציות מרוכבות)

בלינק הבא תמצאו את התירגולים שלי בתורת הפונקציות. תירגלתי את הקורס בחורף 18\19

You can find my tutorial notes in the following link.

 

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: