# Lior Silberman's Math Page

## Publications

(in reverse chronological order)
Title Co-authors Journal  Year  Also available / Remarks
23 Arithmetic quantum unique ergodicity for products of hyperbolic $2$- and $3$-manifolds Zvi Shem-Tov preprint 2022   arXiv:math.DS/2206.05955
22 Singularities of Intertwining Operators and Decompositions of Principal Series Representations Taeuk Nam, Avner Segal J. Lie Theory v. 30 no. 4 2020   arXiv:math.RT/1811.00803
21 The topology of Baumslag-Solitar representations Maxime Bergeron Journal of Topology & Analysis, to appear 2019   arXiv:math.GT/1902.04046
20 Entropy bounds and quantum unique ergodicity for Hecke eigenfunctions on division algebras Akshay Venkatesh CRM Special year proceedings 2019   arXiv:math.NT/1606.02267
19 Volumes of Hyperbolic Three-Manifolds Associated with Modular Links Alexandre Brandts-Longtin, Tali Pinsky Symmetry v. 11 no. 10 art. 1206 2019   arXiv:math.GT/1705.04760
18 An upper bound for the volumes of complements of periodic geodesics Maxime Bergeron, Tali Pinsky IMRN 2019 no. 15, 4707–4729 2017   arXiv:math.GT/1412.2446
17 Homogeneous length functions on groups D.H.J. Polymath Algebra & Number Theory v. 12 no. 7, 1773–1786 2018   arXiv:math.GR/1801.03908 ; further information was posted to the Polymath Wiki
16 Scarring of quasimodes on hyperbolic manifolds Suresh Eswarathasan Nonlinearity v. 31 no. 1 2017   arXiv:math.AP/1609.04912
14 A Note On Nilpotent Representations Maxime Bergeron J. Group Theory v. 19 no. 1, 125–135 2016   arXiv:math.AT/1501.04357
13 Gaussian measures on the of space of Riemannian metrics Brian Clarke, Dmitry Jakobson, Niky Kamran, Jonathan Taylor, Yaiza Canzani Ann. Math. Qué. v.39 no.2, 129–145 2015   arXiv:math.DG/1309.1348
12 Quantum Unique Ergodicity on Locally Symmetric Spaces: the Degenerate Lift   Canad. Math. Bull. v.58 no.3, 632–650 2015   arXiv:math.RT/1104.0074 ; General version of the lift in [4]
11 A uniform spectral gap for congruence covers of a hyperbolic manifold Dubi Kelmer Amer. J. Math. v.135 no.4, 1067–1085 2013   arXiv:math.NT/1010.1010
10 A Haar component for quantum limits on locally symmetric spaces Nalini Anantharaman Israel J. Math. v.195 no.1, 393–447 2013   arXiv:math.GR/1009.4927
9 Poincaré inequalities, embeddings and wild groups Assaf Naor Compos. Math. v.147 no.5, 1546–1572 2011   arXiv:math.GR/1005.4084
8 Finding minimal permutation representations of finite groups Ben Elias and Ramin Takloo-Bighash Exp. Math. v.19 no.1, 121–128 2010   arXiv:math.GR/0705.4122
7 Groups not acting on manifolds David Fisher IMRN 2008 no.16, Art. ID rnn60 2008   arXiv:math.GR/0801.0875
6 Arithmetic quantum chaos on locally symmetric spaces (advisor: Prof. Peter Sarnak) Ph.D. Thesis
(Princeton University)
2005   pdf ; see here for "part of the tree" argument for positive entropy.
4 Quantum Unique Ergodicity for Locally Symmetric Spaces Akshay Venkatesh GAFA v.17 no.3, 960–998 2007   pdf ; ps ; arXiv:math.RT/0407413
3 Addendum to "Random Walk in Random Groups"   GAFA v.13 (2003) no.1, 147–177 2003  (with minor corrections) pdf ; ps
2 Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and Principal Component Analysis Avishai Dekel, Amiram Eldar and Idit Zehavi ApJ 557 no. 1, 102–116 2001   arXiv:astro-ph/0101361
1 Cosmological Density and Power Spectrum from Peculiar Velocities: Principal Component Analysis and Nonlinear Effects (advisor: Prof. Avishai Dekel) B.Sc. Thesis
(Hebrew University)
2000   ps

## Old notes

• (2002) "Expanding Graphs and Groups with Property (T)". This provides (some) motivation for Gromov's construction.
The notes: PDF [also in PS].

• (2001) "Effective Versions of the Chebotarev Density Theorem" by Jeff Lagarias and Andrew Odlyzko, published in the Durham Conference Proceedings 1975.
All the statements in the paper are of the form "there exists a numerical constant c such that...". I wrote a version with the actual constant (no claim to optimality!).
The notes: PS.

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Clarification: the writings on these pages are generally my own creations (to which I own the copyright), and are made available for traditional academic reuse. If you wish to republish substantial portions (including in "derivative works") please ask me for permission. The material is expressly excluded from the terms of UBC Policy 81.