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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:
I study group theory, and especially combinatorial, geometric and probabilistic group theory. Many of the questions in my research involve word measures on groups: measures induced by word maps. This involves the study of free groups and their automorphism group, as well as certain aspects of the representation theory of the groups on which the word measures are induced. In the background there are problems about expansion and spectral gaps of random objects (random graphs, random surfaces, random Cayley graphs and so on).
Groups & Dynamics Seminar: Thursdays at 11:00
Preprints:
Preprints:
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]
An Extension of the Cogrowth Formula to Arbitrary Subsets of the Tree. [arXiv]
Stable Invariants and Their Role in Word Measures on Groups. With Yotam Shomroni. [arXiv]
Papers:
Papers:
The 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, appeared onlineWord 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
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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