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Arxiv:1006.1489V2 [Math.GT] 8 Aug 2010 Ril.Ias Rfie Rmraigtesre Rils[14 Articles Survey the Reading from Profited Also I Article
Pure and Applied Mathematics Quarterly Volume 8, Number 1 (Special Issue: In honor of F. Thomas Farrell and Lowell E. Jones, Part 1 of 2 ) 1—14, 2012 The Work of Tom Farrell and Lowell Jones in Topology and Geometry James F. Davis∗ Tom Farrell and Lowell Jones caused a paradigm shift in high-dimensional topology, away from the view that high-dimensional topology was, at its core, an algebraic subject, to the current view that geometry, dynamics, and analysis, as well as algebra, are key for classifying manifolds whose fundamental group is infinite. Their collaboration produced about fifty papers over a twenty-five year period. In this tribute for the special issue of Pure and Applied Mathematics Quarterly in their honor, I will survey some of the impact of their joint work and mention briefly their individual contributions – they have written about one hundred non-joint papers. 1 Setting the stage arXiv:1006.1489v2 [math.GT] 8 Aug 2010 In order to indicate the Farrell–Jones shift, it is necessary to describe the situation before the onset of their collaboration. This is intimidating – during the period of twenty-five years starting in the early fifties, manifold theory was perhaps the most active and dynamic area of mathematics. Any narrative will have omissions and be non-linear. Manifold theory deals with the classification of ∗I thank Shmuel Weinberger and Tom Farrell for their helpful comments on a draft of this article. I also profited from reading the survey articles [14] and [4]. 2 James F. Davis manifolds. There is an existence question – when is there a closed manifold within a particular homotopy type, and a uniqueness question, what is the classification of manifolds within a homotopy type? The fifties were the foundational decade of manifold theory. -
Mechanical Aspire
Newsletter Volume 6, Issue 11, November 2016 Mechanical Aspire Achievements in Sports, Projects, Industry, Research and Education All About Nobel Prize- Part 35 The Breakthrough Prize Inspired by Nobel Prize, there have been many other prizes similar to that, both in amount and in purpose. One such prize is the Breakthrough Prize. The Breakthrough Prize is backed by Facebook chief executive Mark Zuckerberg and Google co-founder Sergey Brin, among others. The Breakthrough Prize was founded by Brin and Anne Wojcicki, who runs genetic testing firm 23andMe, Chinese businessman Jack Ma, and Russian entrepreneur Yuri Milner and his wife Julia. The Breakthrough Prizes honor important, primarily recent, achievements in the categories of Fundamental Physics, Life Sciences and Mathematics . The prizes were founded in 2012 by Sergey Brin and Anne Wojcicki, Mark Zuckerberg and Priscilla Chan, Yuri and Julia Milner, and Jack Ma and Cathy Zhang. Committees of previous laureates choose the winners from candidates nominated in a process that’s online and open to the public. Laureates receive $3 million each in prize money. They attend a televised award ceremony designed to celebrate their achievements and inspire the next generation of scientists. As part of the ceremony schedule, they also engage in a program of lectures and discussions. Those that go on to make fresh discoveries remain eligible for future Breakthrough Prizes. The Trophy The Breakthrough Prize trophy was created by Olafur Eliasson. “The whole idea for me started out with, ‘Where do these great ideas come from? What type of intuition started the trajectory that eventually becomes what we celebrate today?’” Like much of Eliasson's work, the sculpture explores the common ground between art and science. -
Mathematics Calendar
Mathematics Calendar Please submit conference information for the Mathematics Calendar through the Mathematics Calendar submission form at http:// www.ams.org/cgi-bin/mathcal-submit.pl. The most comprehensive and up-to-date Mathematics Calendar information is available on the AMS website at http://www.ams.org/mathcal/. June 2014 Information: http://www.tesol.org/attend-and-learn/ online-courses-seminars/esl-for-the-secondary- 1–7 Modern Time-Frequency Analysis, Strobl, Austria. (Apr. 2013, mathematics-teacher. p. 429) * 2–30 Algorithmic Randomness, Institute for Mathematical Sciences, 2–5 WSCG 2014 - 22nd International Conference on Computer National University of Singapore, Singapore. Graphics, Visualization and Computer Vision 2014, Primavera Description: Activities 1. Informal Collaboration: June 2–8, 2014. 2. Hotel and Congress Centrum, Plzen (close to Prague), Czech Repub- Ninth International Conference on Computability, Complexity and lic. (Jan. 2014, p. 90) Randomness (CCR 2014): June 9–13, 2014. The conference series 2–6 AIM Workshop: Descriptive inner model theory, American “Computability, Complexity and Randomness” is centered on devel- Institute of Mathematics, Palo Alto, California. (Mar. 2014, p. 312) opments in Algorithmic Randomness, and the conference CCR 2014 2–6 Computational Nonlinear Algebra, Institute for Computational will be part of the IMS programme. The CCR has previously been held and Experimental Research in Mathematics, (ICERM), Brown Univer- in Cordoba 2004, in Buenos Aires 2007, in Nanjing 2008, in Luminy sity, Providence, Rhode Island. (Nov. 2013, p. 1398) 2009, in Notre Dame 2010, in Cape Town 2011, in Cambridge 2012, and in Moscow 2013; it will be held in Heidelberg 2015. 3. Informal 2–6 Conference on Ulam’s type stability, Rytro, Poland. -
3-Manifold Groups
3-Manifold Groups Matthias Aschenbrenner Stefan Friedl Henry Wilton University of California, Los Angeles, California, USA E-mail address: [email protected] Fakultat¨ fur¨ Mathematik, Universitat¨ Regensburg, Germany E-mail address: [email protected] Department of Pure Mathematics and Mathematical Statistics, Cam- bridge University, United Kingdom E-mail address: [email protected] Abstract. We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise. Contents Introduction 1 Chapter 1. Decomposition Theorems 7 1.1. Topological and smooth 3-manifolds 7 1.2. The Prime Decomposition Theorem 8 1.3. The Loop Theorem and the Sphere Theorem 9 1.4. Preliminary observations about 3-manifold groups 10 1.5. Seifert fibered manifolds 11 1.6. The JSJ-Decomposition Theorem 14 1.7. The Geometrization Theorem 16 1.8. Geometric 3-manifolds 20 1.9. The Geometric Decomposition Theorem 21 1.10. The Geometrization Theorem for fibered 3-manifolds 24 1.11. 3-manifolds with (virtually) solvable fundamental group 26 Chapter 2. The Classification of 3-Manifolds by their Fundamental Groups 29 2.1. Closed 3-manifolds and fundamental groups 29 2.2. Peripheral structures and 3-manifolds with boundary 31 2.3. Submanifolds and subgroups 32 2.4. Properties of 3-manifolds and their fundamental groups 32 2.5. Centralizers 35 Chapter 3. 3-manifold groups after Geometrization 41 3.1. Definitions and conventions 42 3.2. Justifications 45 3.3. Additional results and implications 59 Chapter 4. The Work of Agol, Kahn{Markovic, and Wise 63 4.1. -
Meetings & Conferences of The
Meetings & Conferences of the AMS IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See http://www.ams.org/meetings/. Final programs for Sectional Meetings will be archived on the AMS website accessible from the stated URL and in an electronic issue of the Notices as noted below for each meeting. abstract submission form found at http://www.ams.org/ Knoxville, Tennessee cgi-bin/abstracts/abstract.pl. University of Tennessee, Knoxville Algebraic Methods in Graph Theory and Combinator- ics (Code: SS 7A), Felix Lazebnik, University of Delaware, March 21–23, 2014 Andrew Woldar, Villanova University, and Bangteng Xu, Friday – Sunday Eastern Kentucky University. Arithmetic of Algebraic Curves (Code: SS 9A), Lubjana Meeting #1097 Beshaj, Oakland University, Caleb Shor, Western New Eng- Southeastern Section land University, and Andreas Malmendier, Colby College. Associate secretary: Brian D. Boe Commutative Ring Theory (in honor of the retirement Announcement issue of Notices: January 2014 of David E. Dobbs) (Code: SS 1A), David Anderson, Uni- Program first available on AMS website: February 6, 2014 versity of Tennessee, Knoxville, and Jay Shapiro, George Program issue of electronic Notices: March 2014 Mason University. Issue of Abstracts: Volume 35, Issue 2 Completely Integrable Systems and Dispersive Nonlinear Deadlines Equations (Code: SS 12A), Robert Buckingham, University of Cincinnati, and Peter Perry, University of Kentucky. For organizers: Expired Complex Analysis, Probability, and Metric Geometry For abstracts: January 28, 2014 (Code: SS 11A), Matthew Badger, Stony Brook University, Jim Gill, St. -
January 2013 Prizes and Awards
January 2013 Prizes and Awards 4:25 P.M., Thursday, January 10, 2013 PROGRAM SUMMARY OF AWARDS OPENING REMARKS FOR AMS Eric Friedlander, President LEVI L. CONANT PRIZE: JOHN BAEZ, JOHN HUERTA American Mathematical Society E. H. MOORE RESEARCH ARTICLE PRIZE: MICHAEL LARSEN, RICHARD PINK DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY DAVID P. ROBBINS PRIZE: ALEXANDER RAZBOROV TEACHING OF MATHEMATICS RUTH LYTTLE SATTER PRIZE IN MATHEMATICS: MARYAM MIRZAKHANI Mathematical Association of America LEROY P. STEELE PRIZE FOR LIFETIME ACHIEVEMENT: YAKOV SINAI EULER BOOK PRIZE LEROY P. STEELE PRIZE FOR MATHEMATICAL EXPOSITION: JOHN GUCKENHEIMER, PHILIP HOLMES Mathematical Association of America LEROY P. STEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH: SAHARON SHELAH LEVI L. CONANT PRIZE OSWALD VEBLEN PRIZE IN GEOMETRY: IAN AGOL, DANIEL WISE American Mathematical Society DAVID P. ROBBINS PRIZE FOR AMS-SIAM American Mathematical Society NORBERT WIENER PRIZE IN APPLIED MATHEMATICS: ANDREW J. MAJDA OSWALD VEBLEN PRIZE IN GEOMETRY FOR AMS-MAA-SIAM American Mathematical Society FRANK AND BRENNIE MORGAN PRIZE FOR OUTSTANDING RESEARCH IN MATHEMATICS BY ALICE T. SCHAFER PRIZE FOR EXCELLENCE IN MATHEMATICS BY AN UNDERGRADUATE WOMAN AN UNDERGRADUATE STUDENT: FAN WEI Association for Women in Mathematics FOR AWM LOUISE HAY AWARD FOR CONTRIBUTIONS TO MATHEMATICS EDUCATION LOUISE HAY AWARD FOR CONTRIBUTIONS TO MATHEMATICS EDUCATION: AMY COHEN Association for Women in Mathematics M. GWENETH HUMPHREYS AWARD FOR MENTORSHIP OF UNDERGRADUATE -
ANNEXURE 1 School of Mathematics Sciences —A Profile As in March 2010
University Yearbook (Academic Audit Report 2005-10) ANNEXURE 1 School of Mathematics Sciences —A Profile as in March 2010 Contents 1. Introduction 1 1.1. Science Education: A synthesis of two paradigms 2 2. Faculty 3 2.1. Mathematics 4 2.2. Physics 12 2.3. Computer Science 18 3. International Links 18 3.1. Collaborations Set Up 18 3.2. Visits by our faculty abroad for research purposes 19 3.3. Visits by faculty abroad to Belur for research purposes 19 4. Service at the National Level 20 4.1. Links at the level of faculty 20 5. Student Placement 21 5.1. 2006-8 MSc Mathematics Batch 21 5.2. 2008-10 MSc Mathematics Batch 22 6. Research 23 1. Introduction Swami Vivekananda envisioned a University at Belur Math, West Bengal, the headquarters of the Ramakrishna Mission. In his conversation with Jamshedji Tata, it was indicated that the spirit of austerity, service and renun- ciation, traditionally associated with monasticism could be united with the quest for Truth and Universality that Science embodies. An inevitable fruit of such a synthesis would be a vigorous pursuit of science as an aspect of Karma Yoga. Truth would be sought by research and the knowledge obtained disseminated through teach- ing, making knowledge universally available. The VivekanandaSchool of Mathematical Sciences at the fledgling Ramakrishna Mission Vivekananda University, headquartered at Belur, has been set up keeping these twin ide- als in mind. We shall first indicate that at the National level, a realization of these objectives would fulfill a deeply felt National need. 1.1. -
Mathematics in the Austrian-Hungarian Empire
Mathematics in the Austrian-Hungarian Empire Christa Binder The appointment policy in the Austrian-Hungarian Empire In: Martina Bečvářová (author); Christa Binder (author): Mathematics in the Austrian-Hungarian Empire. Proceedings of a Symposium held in Budapest on August 1, 2009 during the XXIII ICHST. (English). Praha: Matfyzpress, 2010. pp. 43–54. Persistent URL: http://dml.cz/dmlcz/400817 Terms of use: © Bečvářová, Martina © Binder, Christa Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz THE APPOINTMENT POLICY IN THE AUSTRIAN- -HUNGARIAN EMPIRE CHRISTA BINDER Abstract: Starting from a very low level in the mid oft the 19th century the teaching and research in mathematics reached world wide fame in the Austrian-Hungarian Empire before World War One. How this was complished is shown with three examples of careers of famous mathematicians. 1 Introduction This symposium is dedicated to the development of mathematics in the Austro- Hungarian monarchy in the time from 1850 to 1914. At the beginning of this period, in the middle of the 19th century the level of teaching and researching mathematics was very low – with a few exceptions – due to the influence of the jesuits in former centuries, and due to the reclusive period in the first half of the 19th century. But even in this time many efforts were taken to establish a higher education. -
Arxiv:2103.09350V1 [Math.DS] 16 Mar 2021 Nti Ae Esuytegopo Iainltransformatio Birational Vue
BIRATIONAL KLEINIAN GROUPS SHENGYUAN ZHAO ABSTRACT. In this paper we initiate the study of birational Kleinian groups, i.e. groups of birational transformations of complex projective varieties acting in a free, properly dis- continuous and cocompact way on an open subset of the variety with respect to the usual topology. We obtain a classification in dimension two. CONTENTS 1. Introduction 1 2. Varietiesofnon-negativeKodairadimension 6 3. Complex projective Kleinian groups 8 4. Preliminaries on groups of birational transformations ofsurfaces 10 5. BirationalKleiniangroupsareelementary 13 6. Foliated surfaces 19 7. Invariant rational fibration I 22 8. InvariantrationalfibrationII:ellipticbase 29 9. InvariantrationalfibrationIII:rationalbase 31 10. Classification and proof 43 References 47 1. INTRODUCTION 1.1. Birational Kleinian groups. 1.1.1. Definitions. According to Klein’s 1872 Erlangen program a geometry is a space with a nice group of transformations. One of the implementations of this idea is Ehres- arXiv:2103.09350v1 [math.DS] 16 Mar 2021 mann’s notion of geometric structures ([Ehr36]) which models a space locally on a geom- etry in the sense of Klein. In his Erlangen program, Klein conceived a geometry modeled upon birational transformations: Of such a geometry of rational transformations as must result on the basis of the transformations of the first kind, only a beginning has so far been made... ([Kle72], [Kle93]8.1) In this paper we study the group of birational transformations of a variety from Klein and Ehresmann’s point of vue. Let Y be a smooth complex projective variety and U ⊂ Y a connected open set in the usual topology. Let Γ ⊂ Bir(Y ) be an infinite group of birational transformations. -
Hermann Cohen's Das Princip Der Infinitesimal-Methode
Hermann Cohen’s Das Princip der Infinitesimal-Methode: The History of an Unsuccessful Book Marco Giovanelli Abstract This paper offers an introduction to Hermann Cohen’s Das Princip der Infinitesimal-Methode (1883), and recounts the history of its controversial reception by Cohen’s early sympathizers, who would become the so-called ‘Marburg school’ of Neo-Kantianism, as well as the reactions it provoked outside this group. By dissecting the ambiguous attitudes of the best-known represen- tatives of the school (Paul Natorp and Ernst Cassirer), as well as those of several minor figures (August Stadler, Kurd Lasswitz, Dimitry Gawronsky, etc.), this paper shows that Das Princip der Infinitesimal-Methode is a unicum in the history of philosophy: it represents a strange case of an unsuccessful book’s enduring influence. The “puzzle of Cohen’s Infinitesimalmethode,” as we will call it, can be solved by looking beyond the scholarly results of the book, and instead focusing on the style of philosophy it exemplified. Moreover, the paper shows that Cohen never supported, but instead explicitly opposed, the doctrine of the centrality of the ‘concept of function’, with which Marburg Neo-Kantianism is usually associated. Long Draft 24/12/2015 Introduction Hermann Cohen’s Das Princip der Infinitesimal-Methode (Cohen, 1883) was undoubtedly an unsuccessful book. Its devastating reviews are customarily mentioned in the literature, but less known and perhaps more significant, is the lukewarm, and sometimes even hostile, reception the book received from Cohen’s early sympathizers. Some members of the group dissented publicly, while others expressed their discomfort in private correspondence. -
Remarks on Non-Euclidean Geometry in the Austro-Hungarian Empire Uwagi O Geometrii Nieeuklidesowej W Monarchii Austro-Węgiersk
TECHNICAL TRANSACTIONS CZASOPISMO TECHNICZNE FUNDAMENTAL SCIENCES NAUKI PODSTAWOWE 1-NP/2014 KATALIN MUNKÁCSY* REMARKS ON NON-EUCLIDEAN GEOMETRY IN THE AUSTRO-HUNGARIAN EMPIRE UWAGI O GEOMETRII NIEEUKLIDESOWEJ W MONARCHII AUSTRO-WĘGIERSKIEJ Abstract Since 1800s, Central European mathematicians have achieved great results in hyperbolic geometry. The paper is devoted to brief description of the background as well as history of these results. Keywords: Austro-Hungarian Empire, history of hyperbolic geometry Streszczenie Od XIX w. matematycy w Europie Środkowo-Wschodniej osiągali znaczące wyniki w geome- trii hiperbolicznej. Niniejszy artykuł zarysowuje tło i historię tych wyników. Słowa kluczowe: Monarchia Austro-Węgierska, historia geometrii hiperbolicznej * Katalin Munkácsy, ELTE TTK Matematikatanítási és Módszertani Központ, Budapest. This paper was prepared for publication by S. Domoradzki and M. Stawiska-Friedland on the basis of the author’s draft. 178 1. Introduction The Bolyai geometry is an important historical phenomenon in mathematics, and a timely research topic with potential applications. I will say a few words about these topics here. I would like to say first something about the expression “Bolyai geometry”. Officially the hyperbolic geometry is called B-L geometry, but this form is not really used anywhere. In 1894 Poincaré was the chairman of the committee that compiled the bibliography of hyperbolic geometry. The title was originally Lobachevsky’s Geometrie. However, it was changed to Geometrie de Bolyai et Lobachevsky – as a result of Hungarian mathematicians’ argumentations (see, e.g. [16]). The most common name is “hyperbolic geometry”; sometimes “Bolyai-Lobachevsky- Gauss” is used. In the Russian-speaking world the common name is ‘Lobachevski’s geometry’, while in Hungary it is called “Bolyai geometry”. -
Mostow and Artin Awarded 2013 Wolf Prize
Mostow and Artin Awarded 2013 Wolf Prize rigidity methods and techniques opened a flood- gate of investigations and results in many related areas of mathematics. Mostow’s emphasis on the “action at infinity” has been developed by many mathematicians in a variety of directions. It had a huge impact in geometric group theory, in the study of Kleinian groups and of low-dimensional topology, and in work connecting ergodic theory and Lie groups. Mostow’s contribution to math- ematics is not limited to strong rigidity theorems. His work on Lie groups and their discrete sub- groups, which was done during 1948–1965, was very influential. Mostow’s work on examples of nonarithmetic lattices in two- and three-dimen- sional complex hyperbolic spaces (partially in Photo: Donna Coveney. Photo: Michael Marsland/Yale. collaboration with P. Deligne) is brilliant and led George D. Mostow Michael Artin to many important developments in mathematics. In Mostow’s work one finds a stunning display of The 2013 Wolf Prize in Mathematics has been a variety of mathematical disciplines. Few math- awarded to: ematicians can compete with the breadth, depth, George D. Mostow, Yale University, “for his and originality of his works. fundamental and pioneering contribution to ge- Michael Artin is one of the main architects ometry and Lie group theory.” of modern algebraic geometry. His fundamental Michael Artin, Massachusetts Institute of contributions encompass a bewildering number Technology, “for his fundamental contributions of areas in this field. to algebraic geometry, both commutative and To begin with, the theory of étale cohomology noncommutative.” was introduced by Michael Artin jointly with Al- The prize of US$100,000 will be divided equally exander Grothendieck.