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:

Office: Manchester 312

Office hours: Tuesday, 11-12

Phone: +972-2-5494937

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].

Arithmeticity and covering rate of the 9-cyclotomic Clifford+

*D*gates in*PU*(3), with Shai Evra, 2024. [arXiv]Ramanujan Bigraphs, with Shai Evra, Brooke Feigon and Kathrin Maurischat, 2023. [arXiv]

Sequential Sweeps and High Dimensional Expansion, with Vedat Levi Alev, 2023. [arXiv]

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

**F**_{2}, 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].