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Professor,
School of Mathematical Sciences,
Tel Aviv University
Room 235
Office hours: By appointment
Office phone: +972-3-640-8235
Email: doronpuder at gmail
In the years 2024-2026 I'm a member in the School of Mathematics, at the Institute for Advanced Study in Princeton.
ERC Project: Word Measures in Groups and Random Cayley Graphs
Research Interests:
Research Interests:
Combinatorial, geometric and probabilistic group theory, representation theory and random matrices, spectral statistics and spectral gaps of random (Schreier/Cayley) graphs and random manifolds.
Groups & Dynamics Seminar: Thursdays at 11:00
Preprints:
Preprints:
Stable Invariants of Words from Random Matrices II: Formulas and Extensions. With Yotam Shomroni. [arXiv]
Strong Convergence of Uniformly Random Permutation Representations of Surface Groups. With Michael Magee and Ramon Van Handel. [arXiv]
Primitivity Testing in Free Group Algebras via Duality. With Matan Seidel and Danielle Ernst-West. [arXiv]
Stable Invariants of Words from Random Matrices. With Yotam Shomroni, and an appendix with Danielle Ernst-West and Matan Seidel. [arXiv]
Papers:
Papers:
An Extension of the Cogrowth Formula to Arbitrary Subsets of the Tree. [arXiv]
Bulletin of the London Mathematical Society, to appearThe Ring of Stable Characters over GL.(q). With Danielle Ernst-West and Yotam Shomroni. [journal, arXiv]
Journal of Algebra, 682, 380--412, 2025On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs. With Gil Alon and Gady Kozma. [journal, arXiv]
Mathematical Proceedings of the Cambridge Philosophical Society, 179 (2), 259--298, 2025Word Measures on GLn(q) and Free Group Algebras. With Danielle Ernst-West and Matan Seidel. [journal, arXiv]
Algebra & Number Theory, 18 (11), 2047--2090, 2024Local Statistics of Random Permutations from Free Products. With Tomer Zimhoni. [journal, arXiv]
International Mathematics Research Notices (IMRN), 2024 (5), 4242--4300, 2024The Asymptotic Statistics of Random Covering Surfaces. With Michael Magee. [journal, arXiv, mini-course (part I, part II, part III, part IV)]
Forum of Mathematics, Pi, 11:e15, 1--51, 2023Matrix Group Integrals, Surfaces, and Mapping Class Groups II: O(n) and Sp(n). With Michael Magee. [journal, arXiv]
Mathematische Annalen, 388, 1437--1494, 2024Core Surfaces. With Michael Magee. [journal, arXiv]
Geometriae Dedicata, 216:46, 2022A Random Cover of a Compact Hyperbolic Surface Has Relative Spectral Gap 3/16-ε. With Michael Magee and Frédéric Naud. [journal, arXiv]
Geometric and Functional Analysis (GAFA), 32, 595--661, 2022Word Measures on Symmetric Groups. With Liam Hanany. [journal, arXiv]
International Mathematics Research Notices (IMRN), 2023 (11), 9221--9297, 2023
Extended abstract in proceedings of FPSAC 2020 [journal, PDF]A Note on the Trace Method for Random Regular Graphs. With Joel Friedman. [journal, arXiv]
Addendum to Expansion of Random Graphs: New Proofs, New Results.
Israel Journal of Mathematics, 256, 269--282, 2023Some Orbits of Free Words that are Determined by Measures on Finite Groups. With Liam Hanany and Chen Meiri. [journal, arXiv]
Journal of Algebra 555, 305--324, 2020
Aldous' Spectral Gap Conjecture for Normal Sets. With Ori Parzanchevski. [journal, arXiv]
Transactions of the American Mathematical Society 373 (10), 7067--7086, 2020
Surface Words are Determined by Word Measures on Groups. With Michael Magee. [journal, arXiv]
Israel Journal of Mathematics 241, 749--774, 2021
Automorphism-Invariant Positive Definite Functions on Free Groups. With Benoît Collins and Michael Magee. [arXiv]
Proceedings of the 27th International Conference in Operator Theory (OT27), 115--137, 2020
Matrix Group Integrals, Surfaces, and Mapping Class Groups I: U(n). With Michael Magee. [journal, arXiv]
Inventiones Mathematicae 218 (2), 341--411, 2019
The Markoff Group of Transformations in Prime and Composite Moduli. With Chen Meiri and appendix by Dan Carmon. [journal, arXiv]
Duke Mathematical Journal 167 (14), 2679--2720, 2018
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 (IMRN) 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]
Expansion of Random Graphs: New Proofs, New Results. [journal, arXiv]
Inventiones Mathematicae 201 (3), 845--908, 2015
Addendum with Joel Friedman: [arXiv]
Measure Preserving Words are Primitive. With Ori Parzanchevski. [journal, arXiv, 50-minute-talk, 4-hours-talk (part I, part II)]
Journal of the American Mathematical Society 28 (1), 63--97, 2015
Growth of Primitive Elements in Free Groups. With Conan Wu. [journal, arXiv, The World of Groups - Question F19 ]
Journal of the London Mathematical Society 90 (1), 89--104, 2014
Stalling Graphs, Algebraic Extensions and Primitive Elements in F2. With Ori Parzanchevski. [journal, arXiv]
Mathematical Proceedings of the Cambridge Philosophical Society 157 (1), 1--11, 2014
Primitive Words, Free Factors and Measure Preservation. [journal, arXiv]
Israel Journal of Mathematics 201 (1), 25--73, 2014
Word Maps and Spectra of Random Graph Lifts. With Nati Linial. [journal, arXiv]
Random Structures and Algorithms 37 (1) 100--135, 2010
Not for publication:
Not for publication:
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.
Book:
Book:
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)
Post-docs:
Post-docs:
Michal Buran (2020-2021)
Daniele Garzoni (2021-2023)
Noam Kolodner (2022- 2024)
Phd Students:
Phd Students:
Matan Seidel (completed 2025)
Danielle Ernst-West
Niv Levhari
Master Students:
Master Students:
Danielle Ernst-West (completed 2019): Word measures on GLn(Fq)
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
Yaron Brodsky (completed 2022): Word Measures on Unitary Groups: Improved Bounds for Small Representations
Tomer Zimhoni (completed 2023): Local statistics of random permutations from free products
Yotam Shomroni (completed 2023): Word Measures on Wreath Products I
Dror Frid
Noam Ta-Shma
Mini-courses in conferences:
Mini-courses in conferences:
In Thematic Program on Randomness and Geometry, Toronto, 29 April - 10 May, 2024
Title: Random covers of graphs and surfacesIn Probabilistic Methods in Negative Curvature, Bangalore, February-March 2023
Title: Random covers of Hyperbolic SurfacesIn Combinatorics of finite-index subgroups, Paris, November 2022
Title: The asymptotic statistics of random covering surfacesIn Paroles, Paroles: A Summer School on Words, Haifa, July 2022
Title: Word measures on symmetric and other groupsIn Group Actions, Geometry and Dynamics, Oholo, July 2022
Title: Free groups, surfaces and linear programmingIn Laplacians on Random Hyperbolic Surfaces and on Random Graphs, Evanston, May 2022
Title: The spectrum of random graphsIn Recent trends in the study of expanders and high dimensional expanders, Rehovot, February 2017
Title: New trends in expanders based on the method of interlacing polynomials
Advanced Classes Taught:
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
Surfaces: Graphs, Groups and Applications - Fall 2021
Advanced seminar in geometric group theory - Spring 2022
Brief CV:
Brief CV:
2024-2025: Von-Neumann fellow, School of Mathematics, IAS, Princeton
2023 - present: Professor, School of Mathematical Sciences, Tel Aviv University
2019-2023: Associate Professor, School of Mathematical Sciences, Tel Aviv University
2016-2019: Senior Lecturer, School of Mathematical Sciences, Tel Aviv University
2014-2016: Member, School of Mathematics, IAS, Princeton
2010-2014: PhD, Einstein Institute of Mathematics, at the Hebrew University of Jerusalem, supervised by Nati Linial.
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