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LIOR ALON

I'm currently a postdoctoral researcher at MIT, hosted by David Jerison, as part of the Simons collaboration on localization of waves.

Previously, I held a postdoc position at IAS (Princeton) from 2020 to 2022, hosted by Peter Sarnak. I received my Ph.D. from 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:

 

A detailed list of publications is found below, as well as nice pictures from these works and other projects. 

My contact - lioralon@mit.edu
Here is my  CV and Research Statement

RESEARCH

PUBLICATIONS

Gap distributions of Fourier quasicrystals via Lee-Yang polynomials
L Alon, A Cohen, and C Vinzant (2024)
Revista Matemática Iberoamericana

Morse theory for discrete magnetic operators and nodal count distribution for graphs

L Alon, M Goresky (2024)

Journal of Spectral Theory

Every real-rooted exponential polynomial is the restriction of a Lee-Yang polynomial

L Alon, A Cohen, and C Vinzant (2023) 

Journal of Functional Analysis 

Generic Laplace eigenfunctions on metric graphs

L Alon (2023)

Journal d'Analyse Mathématique. doi: 10.1007/s11854-023-0308-x

Universality of nodal count distribution in large metric graphs

L Alon, R Band, G Berkolaiko (2022)

Experimental Mathematics
 

Neumann domains on quantum graphs

L Alon, R Band (2021)
Annals of Henri Poincare

 

Neumann domains on graphs and manifolds

L Alon, R Band, M Bersudsky, S Egger (2020)

Analysis and Geometry on Graphs and Manifolds

Nodal statistics on quantum graphs

L Alon, R Band, G Berkolaiko (2017)

Communications in Mathematical Physics
 

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)

PREPRINTS

PH.D. THESIS

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

L Alon

arXiv 2010.03004

VIDEO

ellipticFQC.png

FOURIER QUASICRYSTALS

QUANTUM GRAPHS

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
Berryphase.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. 

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:

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