Doron Puder

Associate Professor,

School of Mathematical Sciences,

Tel Aviv University

Room 235

Office hours: By appointment

Office phone: +972-3-640-8235

Email: doronpuder at gmail


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.

Paroles, Paroles: A Summer School on Words

July 17-21, 2022, Haifa, Israel

Groups & Dynamics Seminar: Thursdays at 11:00

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).

Preprints:

  • Local statistics of random permutations from free products. With Tomer Zimhoni. [arXiv]

  • Word Measures on GLn(Fq) and Free Group Algebras. With Danielle Ernst-West and Matan Seidel, submitted. [arXiv]

  • Core Surfaces. With Michael Magee, submitted. [arXiv]

  • The Asymptotic Statistics of Random Covering Surfaces. With Michael Magee, submitted. [arXiv]

  • Matrix Group Integrals, Surfaces, and Mapping Class Groups II: O(n) and Sp(n). With Michael Magee, submitted. [arXiv]

Papers:

  • A Random Cover of a Compact Hyperbolic Surface Has Relative Spectral Gap 3/16-ε. With Michael Magee and Frédéric Naud. [arXiv]
    Geometric and Functional Analysis (GAFA), accepted for publication

  • Word Measures on Symmetric Groups. With Liam Hanany. [arXiv, Extended abstract - PDF, Extended abstract in proceeding of FPSAC 2020]
    International Mathematics Research Notices, accepted for publication

  • A Note on the Trace Method for Random Regular Graphs. With Joel Friedman. [arXiv]
    Addendum to     Expansion of Random Graphs: New Proofs, New Results.
    Israel Journal of Mathematics, accepted for publication

  • Some 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 2020 (4), 983--1034, 2020

  • Expansion of Random Graphs: New Proofs, New Results. [journal, arXiv]
    Inventiones Mathematicae 201 (3), 845--908, 2015
    Addendum with Joel Friedman: [arXiv]

  • 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:

  • 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:

Post-docs:

Michal Buran (2020-2021)

Daniele Garzoni (2021- )

Phd Students:

Matan Seidel

Danielle Ernst-West

Niv Levhari

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

Yotam Shomroni

Tomer Zimhoni

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