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Hyperbolic Manifolds: an Introduction in 2 and 3 Dimensions Albert Marden Frontmatter More Information
Cambridge University Press 978-1-107-11674-0 - Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions Albert Marden Frontmatter More information HYPERBOLIC MANIFOLDS An Introduction in 2 and 3 Dimensions Over the past three decades there has been a total revolution in the classic branch of mathematics called 3-dimensional topology, namely the discovery that most solid 3-dimensional shapes are hyperbolic 3-manifolds. This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters, and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal proofs. The book is heav- ily illustrated with pictures, mostly in color, that help explain the manifold properties described in the text. Each chapter ends with a set of Exercises and Explorations that both challenge the reader to prove assertions made in the text, and suggest fur- ther topics to explore that bring additional insight. There is an extensive index and bibliography. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-11674-0 - Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions Albert Marden Frontmatter More information [Thurston’s Jewel (JB)(DD)] Thurston’s Jewel: Illustrated is the convex hull of the limit set of a kleinian group G associated with a hyperbolic manifold M(G) with a single, incompressible boundary component. The translucent convex hull is pictured lying over p. 8.43 of Thurston [1979a] where the theory behind the construction of such convex hulls was first formulated. -
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. -
Of the American Mathematical Society August 2017 Volume 64, Number 7
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves -
Image Segmentation Combining Markov Random Fields and Dirichlet Processes
ANR meeting Image segmentation combining Markov Random Fields and Dirichlet Processes Jessica SODJO IMS, Groupe Signal Image, Talence Encadrants : A. Giremus, J.-F. Giovannelli, F. Caron, N. Dobigeon Jessica SODJO ANR meeting 1 / 28 ANR meeting Plan 1 Introduction 2 Segmentation using DP models Mixed MRF / DP model Inference : Swendsen-Wang algorithm 3 Hierarchical segmentation with shared classes Principle HDP theory 4 Conclusion and perspective Jessica SODJO ANR meeting 2 / 28 ANR meeting Introduction Segmentation – partition of an image in K homogeneous regions called classes – label the pixels : pixel i $ zi 2 f1;:::; K g Bayesian approach – prior on the distribution of the pixels – all the pixels in a class have the same distribution characterized by a parameter vector Uk – Markov Random Fields (MRF) : exploit the similarity of pixels in the same neighbourhood Constraint : K must be fixed a priori Idea : use the BNP models to directly estimate K Jessica SODJO ANR meeting 3 / 28 ANR meeting Segmentation using DP models Plan 1 Introduction 2 Segmentation using DP models Mixed MRF / DP model Inference : Swendsen-Wang algorithm 3 Hierarchical segmentation with shared classes Principle HDP theory 4 Conclusion and perspective Jessica SODJO ANR meeting 4 / 28 ANR meeting Segmentation using DP models Notations – N is the number of pixels – Y is the observed image – Z = fz1;:::; zN g – Π = fA1;:::; AK g is a partition and m = fm1;:::; mK g with mk = jAk j A1 A2 m1 = 1 m2 = 5 A3 m3 = 6 mK = 4 AK FIGURE: Example of partition Jessica SODJO ANR -
Lecturenotes 4 MCMC I – Contents
Lecturenotes 4 MCMC I – Contents 1. Statistical Physics and Potts Models 2. Sampling and Re-weighting 3. Importance Sampling and Markov Chain Monte Carlo 4. The Metropolis Algorithm 5. The Heatbath Algorithm (Gibbs Sampler) 6. Start and Equilibration 7. Energy Checks 8. Specific Heat 1 Statistical Physics and Potts Model MC simulations of systems described by the Gibbs canonical ensemble aim at calculating estimators of physical observables at a temperature T . In the following we choose units so that β = 1/T and consider the calculation of the expectation value of an observable O. Mathematically all systems on a computer are discrete, because a finite word length has to be used. Hence, K X (k) Ob = Ob(β) = hOi = Z−1 O(k) e−β E (1) k=1 K X (k) where Z = Z(β) = e−β E (2) k=1 is the partition function. The index k = 1,...,K labels all configurations (or microstates) of the system, and E(k) is the (internal) energy of configuration k. To distinguish the configuration index from other indices, it is put in parenthesis. 2 We introduce generalized Potts models in an external magnetic field on d- dimensional hypercubic lattices with periodic boundary conditions. Without being overly complicated, these models are general enough to illustrate the essential features we are interested in. In addition, various subcases of these models are by themselves of physical interest. Generalizations of the algorithmic concepts to other models are straightforward, although technical complications may arise. We define the energy function of the system by (k) (k) (k) −β E = −β E0 + HM (3) where (k) X (k) (k) (k) (k) 2 d N E = −2 J (q , q ) δ(q , q ) + (4) 0 ij i j i j q hiji N 1 for qi = qj (k) X (k) with δ(qi, qj) = and M = 2 δ(1, qi ) . -
A Brief Survey of the Deformation Theory of Kleinian Groups 1
ISSN 1464-8997 (on line) 1464-8989 (printed) 23 Geometry & Topology Monographs Volume 1: The Epstein birthday schrift Pages 23–49 A brief survey of the deformation theory of Kleinian groups James W Anderson Abstract We give a brief overview of the current state of the study of the deformation theory of Kleinian groups. The topics covered include the definition of the deformation space of a Kleinian group and of several im- portant subspaces; a discussion of the parametrization by topological data of the components of the closure of the deformation space; the relationship between algebraic and geometric limits of sequences of Kleinian groups; and the behavior of several geometrically and analytically interesting functions on the deformation space. AMS Classification 30F40; 57M50 Keywords Kleinian group, deformation space, hyperbolic manifold, alge- braic limits, geometric limits, strong limits Dedicated to David Epstein on the occasion of his 60th birthday 1 Introduction Kleinian groups, which are the discrete groups of orientation preserving isome- tries of hyperbolic space, have been studied for a number of years, and have been of particular interest since the work of Thurston in the late 1970s on the geometrization of compact 3–manifolds. A Kleinian group can be viewed either as an isolated, single group, or as one of a member of a family or continuum of groups. In this note, we concentrate our attention on the latter scenario, which is the deformation theory of the title, and attempt to give a description of various of the more common families of Kleinian groups which are considered when doing deformation theory. -
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 . -
Viable Nash Equilibria: Formation and Defection (Feb 2020)
VIABLE NASH EQUILIBRIA: FORMATION AND DEFECTION (FEB 2020) EHUD KALAI In memory of John Nash Abstract. To be credible, economic analysis should restrict itself to the use of only those Nash equilibria that are viable. To assess the viability of an equilibrium , I study simple dual indices: a formation index, F (), that speci…es the number of loyalists needed to form ; and a defection index, D(), that speci…es the number of defectors that can sustain. Surprisingly, these simple indices (1) predict the performance of Nash equilibria in social systems and lab experiments, and (2) uncover new prop- erties of Nash equilibria and stability issues that have so far eluded game theory re…nements. JEL Classi…cation Codes: C0, C7, D5, D9. 1. Overview Current economic analysis often relies on the notion of a Nash equilibrium. Yet there are mixed opinions about the viability of this notion. On the one hand, many equilibria, referred to as viable in this paper, play critical roles in functioning social systems and perform well in lab and …eld experiments. Date: March 9, 2018, this version Feb 24, 2020. Key words and phrases. Normal form games, Nash equilibrium, Stability, Fault tolerance, Behavioral Economics. The author thanks the following people for helpful conversations: Nemanja Antic, Sunil Chopra, Vince Crawford, K…r Eliaz, Drew Fudenberg, Ronen Gradwohl, Yingni Guo, Adam Kalai, Fern Kalai, Martin Lariviere, Eric Maskin, Rosemarie Nagel, Andy Postlewaite, Larry Samuelson, David Schmeidler, James Schummer, Eran Shmaya, Joel Sobel, and Peyton Young; and seminar participants at the universities of the Basque Country, Oxford, Tel Aviv, Yale, Stanford, Berkeley, Stony Brook, Bar Ilan, the Technion, and the Hebrew University. -
Updating Beliefs When Evidence Is Open to Interpretation: Implications for Bias and Polarization∗
Updating Beliefs when Evidence is Open to Interpretation: Implications for Bias and Polarization∗ Roland G. Fryer, Jr., Philipp Harms, and Matthew O. Jacksony This Version: October 2017 Forthcoming in Journal of the European Economic Association Abstract We introduce a model in which agents observe signals about the state of the world, some of which are open to interpretation. Our decision makers first interpret each signal and then form a posterior on the sequence of interpreted signals. This `double updating' leads to confirmation bias and can lead agents who observe the same information to polarize. We explore the model's predictions in an on-line experiment in which individuals interpret research summaries about climate change and the death penalty. Consistent with the model, there is a significant relationship between an individual's prior and their interpretation of the summaries; and - even more striking - over half of the subjects exhibit polarizing behavior. JEL classification numbers: D10, D80, J15, J71, I30 Keywords: beliefs, polarization, learning, updating, Bayesian updating, biases, dis- crimination, decision making ∗We are grateful to Sandro Ambuehl, Ken Arrow, Tanaya Devi, Juan Dubra, Jon Eguia, Ben Golub, Richard Holden, Lawrence Katz, Peter Klibanoff, Scott Kominers, Franziska Michor, Giovanni Parmigiani, Matthew Rabin, Andrei Shleifer, and Joshua Schwartzein for helpful comments and suggestions. Adriano Fernandes provided exceptional research assistance. yFryer is at the Department of Economics, Harvard University, and the NBER, ([email protected]); Jackson is at the Department of Economics, Stanford University, the Santa Fe Institute, and CIFAR (jack- [email protected]); and Harms is at the Department of Mathematical Stochastics, University of Freiburg, ([email protected]). -
Supplementary Material HR19008 AC
Historical Records of Australian Science © Australian Academy of Science 2020 https://doi.org/10.1071/HR19008_AC Supplementary Material: Historical Records of Australian Science, 2020, 31(1), 17–25 Supplementary material. A bibliography of Australian mathematics to 1960 with observations relating to the history of Australian mathematics Graeme L. Cohen Formerly, School of Mathematical Sciences, University of Technology Sydney, NSW 2007, Australia. Email: [email protected] File S1. Lists List 1—Chronological List of Publications to 1900 2 List 2—Alphabetical by Author List of Publications from 1901 16 to 1960 (Excluding Theses and Most School Books) List 3—Alphabetical by Author List of Theses Leading to the 37 Award of a Higher Degree, to 1960 Index 45 References (further to those in the main text) 56 1 Historical Records of Australian Science © Australian Academy of Science 2020 https://doi.org/10.1071/HR19008_AC Supplementary Material: Historical Records of Australian Science, 2020, 31(1), 17–25 LISTS The main item, article HR19008, should be read first for a full understanding of what is included here. The superscript CAI before an author’s name indicates that biographical information on that author is to be found in Counting Australia In.1 List 1— Chronological List of Publications to 1900 1. RUSSELL, JOHN WM. (18-?) Exercises and examples in expert arithmetic, Kealy & Philip, Sydney. 2. BOWDEN, THOMAS (1812) Bowden’s tables, Ferguson I, 532. [‘Their object is to ascertain at a momentary glance, the difference between sterling and currency … They are calculated with a degree of precision that must have occupied considerable time and attention …’, according to Ferguson. -
James Phelan, Peter J. Rabinowitz, and Robyn Warhol, Series Editors
THEORY AND INTERPRETATION OF NARRATIVE James Phelan, Peter J. Rabinowitz, and Robyn Warhol, Series Editors Narrative Theory Core Concepts and Critical Debates DAVID HERMAN JAMES PHELAN PETER J. RABINOWITZ BRIAN RICHARDSON ROBYN WARHOL THE OHIO STATE UNIVERSITY PRESS | COLUMBUS Copyright © 2012 by The Ohio State University. All rights reserved. Library of Congress Cataloging-in-Publication Data Narrative theory : core concepts and critical debates / David Herman ... [et al.]. p. cm. — (Theory and interpretation of narrative) Includes bibliographical references and index. ISBN 978-0-8142-5184-3 (pbk. : alk. paper) — ISBN 0-8142-5184-6 (pbk. : alk. paper) — ISBN 978-0-8142-1186-1 (cloth : alk. paper) — ISBN 0-8142-1186-0 (cloth : alk. paper) — ISBN 978- 0-8142-9285-3 (cd-rom) 1. Narration (Rhetoric) I. Herman, David, 1962– II. Series: Theory and interpretation of nar- rative series. PN212.N379 2012 808.036—dc23 2011049224 Cover design by James Baumann Text design by Juliet Williams Type set in Adobe Minion Pro Printed by Thomson-Shore, Inc. The paper used in this publication meets the minimum requirements of the American National Standard for Information Sciences—Permanence of Paper for Printed Library Materi- als. ANSI Z39.48–1992. 9 8 7 6 5 4 3 2 1 CONTENTS Preface ix Acknowledgments xiii Part One Perspectives: Rhetorical, Feminist, Mind-Oriented, Antimimetic 1. Introduction: The Approaches Narrative as Rhetoric JAMES PHElan and PETER J. Rabinowitz 3 A Feminist Approach to Narrative RobYN Warhol 9 Exploring the Nexus of Narrative and Mind DAVID HErman 14 Antimimetic, Unnatural, and Postmodern Narrative Theory Brian Richardson 20 2. Authors, Narrators, Narration JAMES PHElan and PETER J. -
Mathematics People, Volume 52, Number 6
Mathematics People Fourier-Mukai transform. He is also working on under- 2005–2006 AMS Centennial standing the structure of cones of divisors on smooth Fellowships Awarded projective varieties by analyzing asymptotic invariants as- sociated to base loci of linear series. He plans to use his The AMS has awarded two Centennial Fellowships for Centennial Fellowship at the University of Michigan and 2005–2006. The recipients are YUAN-PIN LEE of the Univer- the University of Rome, as well as at the University of sity of Utah and MIHNEA POPA of Harvard University. The Chicago. amount of each fellowship is $62,000. The Centennial Please note: Information about the competition for the 2006–2007 AMS Centennial Fellowships will be published in the “Mathematics Opportunities” section of an upcom- ing issue of the Notices. —Allyn Jackson Cerf and Kahn Receive Turing Award The Association for Computing Machinery (ACM) has named VINTON G. CERF and ROBERT E. KAHN the winners of the 2004 A. M. Turing Award, considered the “Nobel Prize of Computing”, for pioneering work on the design and Yuan-Pin Lee Mihnea Popa implementation of the Internet’s basic communications protocols. Cerf is the senior vice president for technology Fellows also receive an expense allowance of $3,000 and strategy at MCI. Kahn is chairman, chief executive officer, a complimentary Society membership for one year. and president of the Corporation for National Research Initiatives (CNRI), a not-for-profit organization for research Yuan-Pin Lee in the public interest on strategic development of Yuan-Pin Lee received his Ph.D. in 1999 from the University network-based information technologies.