Ori Parzanchevski

Hi! I am a faculty member at the Hebrew University of Jerusalem. Previously I was an instructor in Princeton University, and a member at the Institute for Advanced Study. I completed my PhD under the supervision of Alex Lubotzky at the Hebrew University.

Email:

Office: Manchester 312

Office hours: Tuesday 10-11

Phone: +972-2-5494937

Teaching

• Fall 2015 - MAT214: Numbers, Equations and Proofs.

• Fall 2016 - 80830: Representations of Finite Groups.

• Spring 2017 - 80598: Fundamental concepts in representation theory.

• Fall 2017 - From Ramanujan graphs to complexes [Lecture Notes].

• Fall 2018 - Linear Algebra.

• Spring 2019 - Algebraic Structures II.

Papers and preprints

• From Ramanujan Graphs to Ramanujan Complexes. Proceedings of the Ramanujan Centenary Celebration at the Royal Society (Philosophical Transactions A, 378:2163), 2020. With Alex Lubotzky. [final]

• Free flags over local rings and powering of high dimensional expanders. ArXiv:1909.02473, 2019. With Tali Kaufman.

• Cutoff on Ramanujan complexes and classical groups. ArXiv:1901.09383, 2019. With Michael Chapman.

• Random walks on Ramanujan complexes and digraphs. Journal of the European Mathematical Society, to appear, 2019. With Eyal Lubetzky and Alex Lubotzky (not related). [arXiv]

• Ramanujan graphs and digraphs. Analysis and geometry on graphs and manifolds (LMS Lecture Notes), to appear, 2019. [arXiv | book].

• Spectrum and combinatorics of two-dimensional Ramanujan complexes. Israel Journal of Mathematics, 230(2):583–612, 2019. With Konstantin Golubev. [final | web]

• Ramanujan complexes and Golden Gates in PU(3). ArXiv:1810.04710, 2018. With Shai Evra.

• Aldous' spectral gap conjecture for normal sets. ArXiv:1804.02776, 2018. With Doron Puder.

• Super-Golden-Gates for PU(2). Advances in Mathematics, Special volume honoring David Kazhdan, 327:869–901, 2018. With Peter Sarnak. [final]

• Mixing in high-dimensional expanders. Combinatorics, Probability and Computing, 26(5):746-761, 2017. [final].

• Simplicial complexes: spectrum, homology and random walks. Random Structures & Algorithms, 50(2):225–261, 2017. With Ron Rosenthal. [final]

• Isoperimetric inequalities in simplicial complexes. Combinatorica, 36(2):195-227, 2016. With Ron Rosenthal and Ran J. Tessler. [final]

• Measure preserving words are primitive. Journal of the American Mathematical Society, 28(1):63-97, 2015. With Doron Puder. [final]

• Stallings graphs, algebraic extensions and primitive elements in F₂. Mathematical Proceedings of the Cambridge Philosophical Society, 157(1):1-11, 2014. With Doron Puder. [final]

• On the Fourier expansion of word maps. Bulletin of the London Mathematical Society, 46(1):91–102, 2014. With Gili Schul. [final]

• On G-sets and isospectrality. Annales de l'institut Fourier, 63(6):2307-2329, 2013. [final]

• Linear representations and isospectrality with boundary conditions. Journal of Geometric Analysis, 20(2):439–471, 2010. With Ram Band. [final]

• The isospectral fruits of representation theory: quantum graphs and drums. Journal of Physics A: Mathematical and Theoretical, 42:175202, 2009. With Ram Band and Gilad Ben-Shach. [final]

• On tensor products of semistable lattices. ArXiv:1211.3454, 2006. With Ehud de Shalit.