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: Thursdays, 12-13

Phone: +972-2-5494937

Teaching

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

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

Spring 2017 - 80598: Fundamental concepts in representation theory.

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

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

Fall 2020 - Probability I [Whiteboard notes].

Ramanujan complexes and Golden Gates in

*PU*(3).*Geometric and Functional Analysis*, 32:193–235, 2022. With Shai Evra. [final] [code]Free flags over local rings and powering of high dimensional expanders.

*International Mathematics Research Notices*, 2021. With Tali Kaufman. [final]Random walks on Ramanujan complexes and digraphs.

*Journal of the European Mathematical Society*, 22(11):3441–3466, 2020. With Eyal Lubetzky and Alex Lubotzky (not related). [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.

*Transactions of the American Mathematical Society*, 373(10):7067-7086, 2020. With Doron Puder. [final]From Ramanujan graphs to Ramanujan complexes.

*Proceedings of the Ramanujan Centenary Celebration at the Royal Society (Philosophical Transactions A, 378:2163)*, 2019. With Alex Lubotzky. [final]Cutoff on Ramanujan complexes and classical groups. ArXiv:1901.09383, 2019. With Michael Chapman.

Spectrum and combinatorics of two-dimensional Ramanujan complexes.

*Israel Journal of Mathematics*, 230(2):583–612, 2019. With Konstantin Golubev. [final | web]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

**F**_{2}.*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.