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
Teaching
- Fall Semester: Infinitesimal Calculus (2). Lectures take place on Mondays, 12:00--14:00, Tuesdays, 10:00--12:00 and Thursdays, 10:00--12:00 in Hall 7 of the Chemistry Building.
- 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, in my office: room 80 in the Ross building.
Research interests
My areas of research are analysis and mathematical physics, which means that I am interested in analytical problems motivated by physics. My work so far has concentrated around the area of spectral theory. In particular, I study problems related to the spectral properties of random Schrödinger operators and random matrix ensembles, orthogonal polynomials, transport phenomena in complex media and problems connected to spectral geometry.
Publications and preprints
- (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. Erratum in Operators and Matrices, 16 (2022), 1041--1044.
- (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, 25 (2024), 2839--2875.
- (with J. Banks, J. Garza-Vargas, E. Seelig and B. Simon) A useful formula for periodic Jacobi matrices on trees , Proc. Natl. Acad. Sci. USA 121 (2024), Paper No. e2315218121, 4 pp.
- (with E. Seelig) Spectral Gaps for Jacobi Matrices on Graphs , preprint.
- (with D. Ofner) Mesoscopic Universality for Circular Orthogonal Polynomial Ensembles , preprint.
Conferences and workshops organized
