Before joining Tel Aviv University in Fall 2016, I was a member of the School of Mathematics at the Institute for Advanced Study in Princeton for two years, after completing my PhD studies at the Einstein Institute of Mathematics, at the Hebrew University of Jerusalem, under the supervision of Nati Linial.
Word maps and word measures on groups
Random walks and expansion in random graphs and (random) Cayley graphs
Free groups and their automorphism groups
Combinatorial and Geometric Group Theory
Combinatorics and Graph Theory
Asymptotics for a Class of Meandric Systems, via the Hasse Diagram of NC(n). With Alexandru Nica and Ian P. Goulden. [journal, arXiv]
International Mathematics Research Notices 2020 (4), 983--1034, 2020
Ramanujan Coverings of Graphs. With Chris Hall and Will Sawin. [journal, arXiv, STOC (extended abstract)]
Advances in Mathematics 323 ,367--410, 2018
STOC 2016, 48th annual ACM SIGACT Symposium in the Theory of Computing, 533--541, 2016. [Extended abstract]
Preprints / Work in Progress:
Word Measures on Unitary Groups. With Michael Magee. [arXiv]
The results of this preprint have been extended and generalized in the paper "Matrix Group Integrals, Surfaces, and Mapping Class Groups I: U(n)" appearing above. However, this preprint contains useful background, examples and a somewhat different approach in the proofs.
Word Measures on Symmetric Groups. With Liam Hanany. [arXiv, Extended abstract - PDF]
Extended abstract accepted to Proceedings of the 32nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2020).
Asymptotics of Word Measures on GLn(Fq). With Danielle West. In preparation.
Algebraic Structures: Groups, Rings and Fields (Textbook in Hebrew). With Ehud de Shalit and Alex Lubotzky.
מבנים אלגבריים: חבורות, חוגים ושדות
Errata file (please email me about any other mistakes and typos in the book)
Ziv Greenhut (completed 2019): A generation criterion for subsets of special linear groups over finite fields
Gal Ordo (completed 2020): Word measures on the signed symmetric group
Liam Hanany (completed 2021): Word measures on symmetric groups
Advanced Classes Taught:
Random Walks on Groups - Fall 2016
Surfaces: Graphs, Groups and Applications - Spring 2018
Topics in Combinatorial Group Theory - Fall 2018
Representations of Finite Groups - Spring 2020
Introduction to Algebraic Topology - Fall 2020