Hi! I'm a professor at the Department of Mathematics at the Hebrew University of Jerusalem.

Before this I was a Sherman Fairchild Postdoctoral Scholar at the
Department of Mathematics in the
Division of Physics, Mathematics and Astronomy
at Caltech.

I received my PhD from the Department of Mathematics at the Hebrew University of Jerusalem. My advisor was Prof. Yoram Last. My MSc in chemistry was completed under the supervision of Prof. David Avnir, at the Department of Chemistry there.

**Email**: jbreuer /a/t/ math dot huji dot ac dot il

**Office**: Ross building room 80

**Phone**: 02-65-84481

**Mail address**:

Jonathan Breuer

Einstein Institute of Mathematics

Edmond J. Safra Campus, Givat Ram

The Hebrew University of Jerusalem

Jerusalem, 91904

Israel

- Fall Semester: I am on a break from teaching.
- Spring Semester: Differential Equations. Lectures take place on Mondays, 12:00--13:45 in room 217 in the Sprinzak building, and on Tuesdays, 10:00--11:00 in the upper Canada Hall.
- Office hours: Mondays 17:00--17:50, Tuesdays 8:00--9:00, in my office -- room 80 in the Ross building.

- (with D. Avnir) The symmetry numbers of non-rigid molecules, J. Chem. Phys.
**122**(2005), 074110-1 -- 074110-10. - Singular continuous spectrum for the
Laplacian on certain sparse trees, Commun. Math. Phys.
**269**(2007), 851--857. - (with Y. Last) Stability of spectral types for Jacobi matrices under decaying random perturbations, J. Funct. Anal.
**245**(2007), 249--283. - (with P. Forrester and U. Smilansky) Random Schr\"odinger operators from random matrix theory, J. Phys. A: Math. Theor.
**40**(2007) F1--F8. - Singular continuous and dense point spectrum for sparse trees with finite dimensions, Probability and Mathematical Physics (eds. D. Dawson, V. Jaksic and B. Vainberg), CRM Proc. and Lecture Notes
**42**(2007), 65--83. - Localization for the Anderson model on trees with finite dimensions, Ann. Henri Poincarè
**8**(2007), 1507--1520. - Spectral and dynamical properties of certain random Jacobi matrices with growing parameters, Trans. of AMS
**362**(2010), 3161--3182. - (with E. Ryckman and M. Zinchenko) Right limits and reflectionless measures for CMV matrices, Commun. Math. Phys.
**292**(2009), 1--28. - (with R. L. Frank) Singular spectrum for radial trees, Rev. Math. Phys.
**21**(2009), 929--945. - (with Y. Last and B. Simon) The Nevai condition, Constr. Approx.
**32**(2010), 221--254. - (with E. Ryckman and B. Simon) Equality of the spectral and dynamical definitions of reflection, Commun. Math. Phys.
**295**(2010), 531--550. - (with Y. Last and Y. Strauss) Eigenvalue spacings and dynamical upper bounds for discrete one-dimensional Schroedinger operators , Duke Math. J.
**157**(2011), 425--460. - (with B. Simon) Natural boundaries and spectral theory, Adv. Math.
**226**(2011), 4902--4920. - Sine kernel asymptotics for a class of singular measures, J. Approx. Theory
**163**(2011), 1478--1491. - (with E. Strahov) A universality theorem for ratios of random characteristic polynomials, J. Approx. Theory
**164**(2012), 803--814. - (with M. Duits) Nonintersecting paths with a staircase initial condition, Electron. J. Probab.,
**17**(2012), no. 60, 24 pp. - (with M. Keller) Spectral analysis of certain spherically homogeneous graphs, Operators and Matrices,
**7**(2013), 825--847. - (with M. Duits) The Nevai condition and a local law of large numbers for orthogonal polynomial ensembles, Adv. Math.,
**265**(2014), 441--484. - (with Y. Last and B. Simon) Stability of asymptotics of Christoffel-Darboux kernels , Commun. Math. Phys.,
**330**(2014), 1155--1178. - (with M. Duits) Universality of mesoscopic fluctuations for orthogonal polynomial ensembles , Commun. Math. Phys.,
**342**(2016), 491--531. - (with M. Duits) Central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients, J. Amer. Math. Soc.,
**30**(2017), 27--66. - (with B. Simon and O. Zeitouni) Large deviations and sum rules for spectral theory - a pedagogical approach, J. Spect. Theory,
**8**(2018), 1551--1581. - (with B. Simon and O. Zeitouni) Large deviations and the Lukic conjecture , Duke Math J.,
**167**(2018), 2857--2902. - (with S. Denisov and L. Eliaz) On the essential spectrum of Schroedinger operators on trees , Math. Phys. Anal. Geom.,
**21**(2018), 25pp. - (with D. Weissman) Level repulsion for Schroedinger operators with singular continuous spectrum , J. Spect. Theory,
**9**(2019), 429--451. - (with N. Levi) On the decomposition of the Laplacian on metric graphs , Ann. Henri Poincarè,
**21**(2020), 499--537. - (with N. Avni and B. Simon) Periodic Jacobi matrices on trees , Adv. Math.,
**370**(2020), 42pp. - (with E. Seelig) On the spacing of zeros of paraorthogonal polynomials for singular measures , J. Approx. Theory,
**259**(2020), 20pp. - Scaling limits of Jacobi matrices and the Christoffel-Darboux kernel , Constr. Approx.,
**53**(2021), 349--379. - (with Y. Grinshpon and M. White) Spectral fluctuations for Schroedinger operators with a random decaying potential , Ann. Henri Poincarè,
**22**(2021), 3763--3794. - (with N. Avni, G. Kalai and B. Simon) Periodic boundary conditions for periodic Jacobi matrices on trees , Pure and Applied Functional Analysis,
**7**(2022), 489--502 (issue dedicated to Shmuel Agmon on his 100th Birthday). - (with H. Kovarik) Resonances at the threshold for Pauli operators in dimension two , Ann. Henri Poincarè, to appear.
- (with J. Banks, J. Garza-Vargas, E. Seelig and B. Simon) A useful formula for periodic Jacobi matrices on trees , preprint.
- (with E. Seelig) Spectral Gaps for Jacobi Matrices on Graphs , preprint.

- Quantum Spectra and Transport , June 30--July 4, 2013, The Hebrew University of Jerusalem, Israel.

- Random Matrices and Jacobi Operators , May 19--May 23, 2014, The Mittag-Leffler Institute, Sweden.

- Session on Quantum Mechanics and Spectral Theory in the XVIII International Congress on Mathematical Physics , July 27--August 1, 2015, Santiago de Chile.

- Spectral Theory of Quasi-Periodic and Random Operators , November 12--November 16, 2018, CRM, Montreal, Canada.

- The 24th Midrasha Mathematicae: Random Schroedinger Operators and Random Matrices , May 14--May 18, 2023, The Israel Institute for Advanced Studies, Jerusalem, Israel.

- Random Matrices and Integrability in Complex and Quantum Systems , June 26--July 01, 2024, Yad Hashmona, Israel.