Doron Puder

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.

Research Interests:

• 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

Papers:

• 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. [arXiv]
  Israel Journal of Mathematics, to appear

• 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), to appear

• 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

• 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] Addendum: [arXiv]
  Inventiones Mathematicae 201 (3), 845--908, 2015

• 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

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.

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

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

• A Random Cover of a Compact Hyperbolic Surface Has Relative Spectral Gap 3/16-ε. With Michael Magee and Frédéric Naud, submitted. [arXiv]

• 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).

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

• Asymptotics of Word Measures on GL_n(F_q). With Danielle West. In preparation.

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)

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