Lie Groups and Ergodic Theory

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Citations From References: 0 Previous Up Next Book From Reviews: 0 MR1699355 (2000b:00011) 00B25 (22-06 28-06) FLie groups and ergodic theory. Proceedings of the International Colloquium held in Mumbai, January 4–12, 1996. Edited by S. G. Dani. Tata Institute of Fundamental Research Studies in Mathematics, 14. Published for the Tata Institute of Fundamental Research, Bombay; by Narosa Publishing House, New Delhi, 1998. viii+386 pp. $32.00. ISBN 81-7319-235-9 Contents: Martine Babillot and François Ledrappier, Geodesic paths and horocycle flow on abelian covers (1–32); J. R. Choksi and M. G. Nadkarni, On the question of transformations with sim- ple Lebesgue spectrum (33–57); S. G. Dani and C. R. E. Raja, Asymptotics of measures under group automorphisms and an application to factor sets (59–73); Alex Eskin and Benson Farb, Quasi-flats in H2 × H2 (75–103); Hillel Furstenberg [Harry Furstenberg], Stiffness of group actions (105–117); Dmitry Y.Kleinbock, Bounded orbits conjecture and Diophantine approximation (119–130); Alexander Lubotzky and Robert J. Zimmer, A canonical arithmetic quotient for sim- ple Lie group actions (131–142); Shahar Mozes, On the congruence subgroup problem for tree lattices (143–149); Hee Oh, Arithmetic properties of some Zariski dense discrete subgroups (151– 165); Marina Ratner, On the p-adic and S-arithmetic generalizations of Raghunathan’s conjectures (167–202); Klaus Schmidt [Klaus Schmidt1], On the cohomology of algebraic Zd-actions with values in compact Lie groups (203–228); Nimish A. Shah, Invariant measures and orbit closures on homogeneous spaces for actions of subgroups generated by unipotent elements (229–271); Yehuda Shalom, Random ergodic theorems, invariant means and unitary representation (273– 314); G. A. Soifer, Structure of infinite index maximal subgroups of SLn(Z) (315–324); A. N. Starkov, Dynamics of non-unipotent homogeneous flows (325–343); William A. Veech, Geomet- ric realizations of hyperelliptic curves. II (345–365); Dave Witte [David Riley Witte], Cocycle superrigidity for ergodic actions of non-semisimple Lie groups (367–386). {The papers are being reviewed individually.} c Copyright American Mathematical Society 2000, 2010.

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Short CV For: Alexander Lubotzky
Short CV for: Alexander Lubotzky Personal: • born 28/6/56 in Israel. • Married to Yardenna Lubotzky (+ six children) Studies: • B. Sc., Mathematics, Bar-Ilan University, 1975. • Ph.D., Mathematics, Bar-Ilan University, 1979. (Supervisor: H. Fussten- berg, Thesis: Proﬁnite groups and the congruence subgroup problem.) Employment: • 1982 - current: Institute of Mathematics, Hebrew University of Jerusalem; Professor - Holding the Maurice and Clara Weil Chair in Mathematics • 1999-current: Adjunct Professor at Yale University • Academic Year 2005-2006: Leading a year long research program at the Institute for Advanced Study in Princeton on \Lie Groups, Repre- sentations and Discrete Mathematics." Previous Employment: • Bar-Ilan University, 1976-1982 • Israeli Defense Forces, 1977-1982 • Member of the Israeli Parliament (Knesset), 1996-1999 Visiting Positions: • Yale University (several times for semesters or years) • Stanford University (84/5) • University of Chicago (92/3) • Columbia University (Elenberg visiting Professor Fall 2000) 1 • Institute for Advanced Study, Princeton (2005/6) Main prizes and Academic Honors: • Elected as Foreign Honorary member of the American Academy of Arts and Sciences • Ferran Sunyer i Balaguer Prize twice: 1993 for the book: \Discrete Groups, Expanding Groups and Invariant Measures", Prog. in math 125, Birkhauser 1994, and in 2002 joint with Professor Dan Segal from Oxford for the book \Subgroup Growth", Prog. in Math. 212, Birkhauser 2003. • The Rothschild Prize 2002. • The Erdos Prize in 1991. Editorial work: • Israel Journal of Mathematics (1990-now) • Journal of Algebra (1990-2005) • GAFA (1990-2000) • European Journal of Combinatorics • Geometric Dedicata • Journal of the Glasgow Mathematical Scientists Books and papers: • Author of 3 books and over 90 papers.
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A Group Theoretic Characterization of Linear Groups
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector JOURNAL OF ALGEBRA 113, 207-214 (1988) A Group Theoretic Characterization of Linear Groups ALEXANDER LUBOTZKY Institute qf Mathematics, Hebrew University, Jerusalem, Israel 91904 Communicated by Jacques Tits Received May 12, 1986 Let r be a group. When is f linear? This is an old problem. The first to study this question systematically was Malcev in 1940 [M], who essen- tially reduced the problem to finitely generated groups. (Note that a finitely generated group is linear over some field of characteristic zero if and only if it can be embedded in CL,(C) for some n.) Very little progress was made since that paper of Malcev, although, as linear groups are a quite special type of group, many necessary conditions were obtained, e.g., r should be residually finite and even virtually residually-p for almost all primes p, f should be virtually torsion free, and if not solvable by finite it has a free non-abelian subgroup, etc. (cf. [Z]). Of course, none of these properties characterizes the finitely generated linear groups over @. In this paper we give such a characterization using the congruence structure of r. First some definitions: For a group H, d(H) denotes the minimal number of generators for H. DEFINITION. Let p be a prime and c an integer. A p-congruence structure (with a bound c) for a group r is a descending chain of finite index normal subgroups of r = N, 2 N, 2 N, z .
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Counting Arithmetic Lattices and Surfaces
ANNALS OF MATHEMATICS Counting arithmetic lattices and surfaces By Mikhail Belolipetsky, Tsachik Gelander, Alexander Lubotzky, and Aner Shalev SECOND SERIES, VOL. 172, NO. 3 November, 2010 anmaah Annals of Mathematics, 172 (2010), 2197–2221 Counting arithmetic lattices and surfaces By MIKHAIL BELOLIPETSKY, TSACHIK GELANDER, ALEXANDER LUBOTZKY, and ANER SHALEV Abstract We give estimates on the number ALH .x/ of conjugacy classes of arithmetic lattices of covolume at most x in a simple Lie group H . In particular, we obtain a first concrete estimate on the number of arithmetic 3-manifolds of volume at most x. Our main result is for the classical case H PSL.2; R/ where we show D that log AL .x/ 1 lim H : x x log x D 2 !1 The proofs use several different techniques: geometric (bounding the number of generators of as a function of its covolume), number theoretic (bounding the number of maximal such ) and sharp estimates on the character values of the symmetric groups (to bound the subgroup growth of ). 1. Introduction Let H be a noncompact simple Lie group with a fixed Haar measure .A discrete subgroup of H is called a lattice if . H / < . A classical theorem of n 1 Wang[Wan72] asserts that if H is not locally isomorphic to PSL2.R/ or PSL2.C/, then for every 0 < x R the number LH .x/ of conjugacy classes of lattices in H of 2 covolume at most x is finite. This result was greatly extended by Borel and Prasad [BP89]. In recent years there has been an attempt to quantify Wang’s theorem and to give some estimates on LH .x/ (see[BGLM02],[Gel04],[GLNP04],[Bel07] and[BL]).
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IMU Secretary An: [email protected]; CC: Betreff: IMU EC CL 05/07: Vote on ICMI Terms of Reference Change Datum: Mittwoch, 24
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Graduate School of Arts and Sciences 2013–2014
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A Biography of Leon Ehrenpreis
Developments in Mathematics VOLUME 28 Series Editors: Krishnaswami Alladi, University of Florida Hershel M. Farkas, Hebrew University of Jerusalem Robert Guralnick, University of Southern California For further volumes: http://www.springer.com/series/5834 Hershel M. Farkas • Robert C. Gunning Marvin I. Knopp • B.A. Taylor Editors From Fourier Analysis and Number Theory to Radon Transforms and Geometry In Memory of Leon Ehrenpreis 123 Editors Hershel M. Farkas Robert C. Gunning Einstein Institute of Mathematics Department of Mathematics The Hebrew University of Jerusalem Princeton University Givat Ram, Jerusalem Princeton, NJ Israel USA Marvin I. Knopp B.A. Taylor Department of Mathematics Department of Mathematics Temple University University of Michigan Philadelphia, PA Ann Arbor, MI USA USA ISSN 1389-2177 ISBN 978-1-4614-4074-1 ISBN 978-1-4614-4075-8 (eBook) DOI 10.1007/978-1-4614-4075-8 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012944371 © Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
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Read Ebook {PDF EPUB} from the Wilderness and Lebanon an Israeli Soldier's Story of War and Recovery by Asael Lubotzky Asael Lubotzky
Read Ebook {PDF EPUB} From the Wilderness and Lebanon An Israeli Soldier's Story of War and Recovery by Asael Lubotzky Asael Lubotzky. ,est un ancien militaire israélien blessé au combat, devenu médecin ( « עשהאל לובוצקי » : Asaël Lubotzky , ( Assaël Loubotzky , en hébreu romancier et biologiste. Sommaire. Biographie. Asael Lubotzky est né et a grandi à Efrat, puis a étudié à la Yechiva Hesder à Ma'aleh Adumim. Il été accepté dans l'unité d'élite de la Marine israélienne Shayetet 13, mais a préféré s'enrôler dans le 51 e bataillon de la Brigade Golani. Il suivit une formation militaire et fut choisi comme cadet exceptionnel de la compagnie. Après avoir terminé l'école des officiers, Lubotzky est nommé commandant d'un peloton de la brigade Golani [ 1 ] . Il a mené sa section dans les combats à Gaza et, au cours de la Seconde guerre du Liban, a pris part à de nombreux combats au cours desquels plusieurs de ses camarades ont été tués et blessés, jusqu'à ce que lui aussi soit gravement blessé à la Bataille de Bint Jbeil et soit devenu handicapé [ 2 ] . Après sa rééducation, il a commencé à étudier la médecine à la faculté de médecine de l’Université hébraïque Hadassah [ 3 ] . Il s'est spécialisé en pédiatrie à l’hôpital Shaare Zedek de Jérusalem et a terminé son doctorat à l’Université hébraïque. Les recherches de Lubotzky sont axées sur les liens entre l’ADN et le cancer [ 4 ] . Le premier livre de Lubotzky, From the Wilderness and Lebanon [ 5 ] , décrivant ses expériences de guerre et sa réhabilitation, a été publié en 2008 d'abord en feuilleton dans le journal Yedioth Ahronoth , est devenu un best-seller [ 6 ] , a suscité des éloges de la part des critiques et a été traduit en anglais [ 7 ] .
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The Rise of the Zionist Right: Polish Jews and the Betar Youth Movement, 1922-1935
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