Ori Parzanchevski

Hi! I am an associate professor 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 in 2014.

Email:

Teaching

• MAT214: Numbers, Equations and Proofs / 80115: Elementary Number Theory [Notes].

• Fall 2016 - 80830: Representations of Finite Groups [Exercises].

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

• Spring 2020 - Expander graphs [Whiteboard notes and exercises].

• Fall 2020 - Probability I [Whiteboard notes].

• Spring 2022 - Matrix Lie groups [Notes and exercises].

• Spring 2023 - p-adic groups [Notes and exercises].

Papers and preprints

• Geometry over finite local rings: Rigidity and Isospectrality, with Yishai Lavi, 2025. [arXiv]

• Optimal generators for matrix groups, 2025. [draft]

• Multi-Qubit Golden Gates, with Rahul Dalal and Shai Evra, 2025. [arXiv]

• Arithmeticity, thinness and efficiency of qutrit Clifford+T gates, with Shai Evra, 2024. [arXiv]

• Sequential Sweeps and High Dimensional Expansion, with Vedat Levi Alev. [arXiv]
  30th International Conference on Randomization and Computation (RANDOM 2026). [RANDOM]

• Ramanujan Bigraphs, with Shai Evra, Brooke Feigon and Kathrin Maurischat, 2023. [arXiv]
  Anouncement in Comptes Rendus Mathématique, 364:71-78, 2026 [CRM]
  Extended abstract at the 66th Symposium on Foundations of Computer Science (FOCS 2025) [FOCS].

• Cutoff on Ramanujan complexes and classical groups, with Michael Chapman.
  Commentarii Mathematici Helvetici, 97(3):431–456, 2022. [final]

• Ramanujan complexes and Golden Gates in PU(3), with Shai Evra.
  Geometric and Functional Analysis, 32:193–235, 2022. [final] [code]

• Free flags over local rings and powering of high dimensional expanders, with Tali Kaufman.
  International Mathematics Research Notices, 2022(19):14741–14769, 2022. [final]

• Random walks on Ramanujan complexes and digraphs, with Eyal Lubetzky and Alex Lubotzky (not related).
  Journal of the European Mathematical Society, 22(11):3441–3466, 2020. [final]

• Ramanujan graphs and digraphs.
  In Analysis and geometry on graphs and manifolds, LMS Lecture Notes 461, 2020. [arXiv | final].

• Aldous' spectral gap conjecture for normal sets, with Doron Puder.
  Transactions of the American Mathematical Society, 373(10):7067-7086, 2020. [final]

• From Ramanujan graphs to Ramanujan complexes, with Alex Lubotzky.
  Proceedings of the Ramanujan Centenary Celebration at the Royal Society (Philosophical Transactions A, 378:2163), 2019. [final]

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

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

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

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

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

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

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

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

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

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

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

• On tensor products of semistable lattices, with Ehud de Shalit, 2006 [arXiv].