NOTICES Was Sent to Press, the Meeting Dates Which Fall Rather Far in the Future Are Subject Tr Change
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In the Fall of 1977, He Researched and Conducted a Seminar In
The Bakke Case and the University of Pennsylvania (Meyerson) SPEAKING OUT " NEWS " GRANT DEADLINES LEAVES " United Way " THINGS TO DO SUPPLEMENT: Bakke Brief Published Weekly by the University of Pennsylvania Volume 24, Number 8 October 25, 1977 FREEZE ON HIRING The State appropriation request for the University includes million for On October 21, President Martin Meyerson put into effect the approximately $7 the Medical, Dental and Veterinary schools and million for student aid and first in a series of contingency actions to deal with the $10 general instruction, which is divided the rest of the appropriation and tax impasse in Harrisburg: a suspension of all among University's programs. The Senate has for hiring and internal transfer of staff. On the same day a group of already passed non-preferred appropriations Penn State. and Lincoln. The faculty Senate leaders and deans began a series of meetings with Temple, Pittsburgh Legislature meantime must still find a of the the Provost and the President on steps for dealing with the way funding appropriations. financial future. University's BAKKE BRIEF: IN ALMANAC HARRISBURG: CALL FOR REVERSAL In this issue Almanac publishes the full text of the Bakke Brief The Pennsylvania State Senate is expected to decide before (see supplement). There is also a statement by President Meyerson Friday whether to vote again on the $17 million appropriation bill explaining how the brief came into being and why he felt it was for the University. The Legislature is scheduled to recess Thursday important for the University to take this stand (page 2). evening until November 14. -
Contemporary Mathematics 442
CONTEMPORARY MATHEMATICS 442 Lie Algebras, Vertex Operator Algebras and Their Applications International Conference in Honor of James Lepowsky and Robert Wilson on Their Sixtieth Birthdays May 17-21, 2005 North Carolina State University Raleigh, North Carolina Yi-Zhi Huang Kailash C. Misra Editors http://dx.doi.org/10.1090/conm/442 Lie Algebras, Vertex Operator Algebras and Their Applications In honor of James Lepowsky and Robert Wilson on their sixtieth birthdays CoNTEMPORARY MATHEMATICS 442 Lie Algebras, Vertex Operator Algebras and Their Applications International Conference in Honor of James Lepowsky and Robert Wilson on Their Sixtieth Birthdays May 17-21, 2005 North Carolina State University Raleigh, North Carolina Yi-Zhi Huang Kailash C. Misra Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeTurck, managing editor George Andrews Andreas Blass Abel Klein 2000 Mathematics Subject Classification. Primary 17810, 17837, 17850, 17865, 17867, 17868, 17869, 81T40, 82823. Photograph of James Lepowsky and Robert Wilson is courtesy of Yi-Zhi Huang. Library of Congress Cataloging-in-Publication Data Lie algebras, vertex operator algebras and their applications : an international conference in honor of James Lepowsky and Robert L. Wilson on their sixtieth birthdays, May 17-21, 2005, North Carolina State University, Raleigh, North Carolina / Yi-Zhi Huang, Kailash Misra, editors. p. em. ~(Contemporary mathematics, ISSN 0271-4132: v. 442) Includes bibliographical references. ISBN-13: 978-0-8218-3986-7 (alk. paper) ISBN-10: 0-8218-3986-1 (alk. paper) 1. Lie algebras~Congresses. 2. Vertex operator algebras. 3. Representations of algebras~ Congresses. I. Leposwky, J. (James). II. Wilson, Robert L., 1946- III. Huang, Yi-Zhi, 1959- IV. -
About Lie-Rinehart Superalgebras Claude Roger
About Lie-Rinehart superalgebras Claude Roger To cite this version: Claude Roger. About Lie-Rinehart superalgebras. 2019. hal-02071706 HAL Id: hal-02071706 https://hal.archives-ouvertes.fr/hal-02071706 Preprint submitted on 18 Mar 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. About Lie-Rinehart superalgebras Claude Rogera aInstitut Camille Jordan ,1 , Universit´ede Lyon, Universit´eLyon I, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France Keywords:Supermanifolds, Lie-Rinehart algebras, Fr¨olicher-Nijenhuis bracket, Nijenhuis-Richardson bracket, Schouten-Nijenhuis bracket. Mathematics Subject Classification (2010): .17B35, 17B66, 58A50 Abstract: We extend to the superalgebraic case the theory of Lie-Rinehart algebras and work out some examples concerning the most popular samples of supermanifolds. 1 Introduction The goal of this article is to discuss some properties of Lie-Rinehart structures in a superalgebraic context. Let's first sketch the classical case; a Lie-Rinehart algebra is a couple (A; L) where L is a Lie algebra on a base field k, A an associative and commutative k-algebra, with two operations 1. (A; L) ! L denoted by (a; X) ! aX, which induces a A-module structure on L, and 2. -
Mathematisches Forschungsinstitut Oberwolfach Enveloping Algebras
Mathematisches Forschungsinstitut Oberwolfach Report No. 13/2005 Enveloping Algebras and Geometric Representation Theory Organised by Shrawan Kumar (Chapel Hill) Peter Littelmann (Wuppertal) Wolfgang Soergel (Freiburg) March 13th – March 19th, 2005 Abstract. The study of Enveloping Algebras has undergone a significant and con- tinuous evolution and moreover has inspired a wide variety of developments in many areas of mathematics including Ring Theory, Differential Operators, Invariant Theory, Quantum Groups and Hecke Algebras. The aim of the workshop was to bring together researchers from diverse but highly interre- lated subjects to discuss new developments and bring forward the research in this whole area by fostering the scientific interaction. Mathematics Subject Classification (2000): 17xx, 22xx, 81xx. Introduction by the Organisers Since its inception in the early seventies, the study of Enveloping Algebras has undergone a significant and continuous evolution and moreover has inspired a wide variety of developments in many areas of mathematics including Ring Theory, Differential Operators, Invariant Theory, Quantum Groups and Hecke Algebras. As indicated above, one of the main goals behind this meeting was to bring together a group of participants with a wide range of interests in and around the geometric and the combinatorial side of the representation theory of Lie groups and algebras. We strongly believe that such an approach to representation theory, in particular interaction between geometry and representation theory, will open up new avenues of thought and lead to progress in a number of areas. This diversity was well reflected in the expertize represented by the conference participants, as well as in the wide range of topics covered. -
Irving Ezra Segal (1918–1998)
mem-segal.qxp 5/12/99 12:57 PM Page 659 Irving Ezra Segal (1918–1998) John C. Baez, Edwin F. Beschler, Leonard Gross, Bertram Kostant, Edward Nelson, Michèle Vergne, and Arthur S. Wightman Irving Segal died suddenly on August 30, 1998, After the war while taking an evening walk. He was seventy-nine Segal spent two and was vigorously engaged in research. years at the Insti- Born on September 13, 1918, in the Bronx, he tute for Advanced grew up in Trenton and received his A.B. from Study, where he Princeton in 1937. What must it have been like to held the first of the be a member of the Jewish quota at Princeton in three Guggenheim the 1930s? He told me once that a fellow under- Fellowships that he graduate offered him money to take an exam in his was to win. Other stead and was surprised when Irving turned him honors included down. election to the Na- He received his Ph.D. from Yale in 1940. His the- tional Academy of sis was written under the nominal direction of Sciences in 1973 Einar Hille, who suggested that Segal continue his and the Humboldt Award in 1981. At and Tamarkin’s investigation of the ideal theory the University of of the algebra of Laplace-Stieltjes transforms ab- Chicago from 1948 solutely convergent in a fixed half-plane. But, Segal to 1960, he had fif- wrote, “For conceptual clarification and for other teen doctoral stu- reasons, an investigation of the group algebra of dents, and at MIT, a general [locally compact] abelian group was of where he was pro- Irving Segal interest.” And the thesis was not restricted to fessor from 1960 abelian groups. -
Fedosov's Quantization of Semisimple Coadjoint Orbits
Fedosov's quantization of semisimple coadjoint orbits. by Alexander Astashkevich Submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 1996 @ Massachusetts Institute of Technology 1996. All rights reserved. Author .............................. ..... , ....................... Department of Mathematics May 1, 1996 Certified by. x.... Bertram Kostant Professor Thesis Supervisor Accepted by ........ .... .............. ...... ........ David Vogan Chairman, Departmental Committee on Graduate Students SCIENCE MA ;C t4 J :-:, t;,2 .'I•--_ B ~996 Fedosov's quantization of semisimple coadjoint orbits. by Alexander Astashkevich Submitted to the Department of Mathematics on May 1, 1996, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract In this thesis, we consider Fedosov's quantization (C"(0)[[h]], *) of the functions on a coadjoint orbit 0 of a Lie group G corresponding to the trivial cohomology class in H 2 (O, IR[[h]]) and G-invariant torsion free symplectic connection on 0 (when it exists). We show that the map g X -+ IX eC' (0)[[h]] is a homomorphism of Lie algebras, where we consider kC'(0) [[h]] as a Lie algebra with the bracket [f, g] = fg- gff,, g EC"C'(0)[[h]]. This map defines an algebra homomorphism A from U(g)((h)) to the algebra C~"(0)((h)). We construct a representation of Co((0)((h)). In case G is a simple Lie group and O is a semisimple coadjoint orbit, we show that p maps U(g)((h)) onto the algebra of polynomial functions on 0 endowed with a star product. -
Council Congratulates Exxon Education Foundation
from.qxp 4/27/98 3:17 PM Page 1315 From the AMS ics. The Exxon Education Foundation funds programs in mathematics education, elementary and secondary school improvement, undergraduate general education, and un- dergraduate developmental education. —Timothy Goggins, AMS Development Officer AMS Task Force Receives Two Grants The AMS recently received two new grants in support of its Task Force on Excellence in Mathematical Scholarship. The Task Force is carrying out a program of focus groups, site visits, and information gathering aimed at developing (left to right) Edward Ahnert, president of the Exxon ways for mathematical sciences departments in doctoral Education Foundation, AMS President Cathleen institutions to work more effectively. With an initial grant Morawetz, and Robert Witte, senior program officer for of $50,000 from the Exxon Education Foundation, the Task Exxon. Force began its work by organizing a number of focus groups. The AMS has now received a second grant of Council Congratulates Exxon $50,000 from the Exxon Education Foundation, as well as a grant of $165,000 from the National Science Foundation. Education Foundation For further information about the work of the Task Force, see “Building Excellence in Doctoral Mathematics De- At the Summer Mathfest in Burlington in August, the AMS partments”, Notices, November/December 1995, pages Council passed a resolution congratulating the Exxon Ed- 1170–1171. ucation Foundation on its fortieth anniversary. AMS Pres- ident Cathleen Morawetz presented the resolution during —Timothy Goggins, AMS Development Officer the awards banquet to Edward Ahnert, president of the Exxon Education Foundation, and to Robert Witte, senior program officer with Exxon. -
Mathematicians at Stockholm, the Council of the Society Will Meet Sweden
AMERICAN MATHEMATICAL SOCIETY VOLUME 9, NUMBER 4 ISSUE NO. 62 AUGUST 1962 THE AMERICAN MATHEMATICAL SOCIETY Edited by John W. Green and Gordon L. Walker CONTENTS MEETINGS Calendar of Meetings .•.......•.•.•...•.....•......••••.•. 248 Program of the Summer Meeting in Vancouver, B. C .•.............. 249 Abstracts of the Meeting - pages 284-313 PRELIMINARY ANNOUNCEMENT OF MEETING •..•.••...........•..•. 263 ACTIVITIES OF OTHER ASSOCIATIONS .••.••••..•.....•.........••• 265 NEWS ITEMS AND ANNOUNCEMENTS .••.•.....••.....•.•. 262, 267,276 PERSONAL ITEMS .•..•.••.....•.•.•.•.....................•. 268 NEW AMS PUBLICATIONS •.....•..••••.....•••....•.....•.•...• 273 LETTERS TO THE EDITOR ....•....•....•.......•..••.......•.. 274 MEMORANDA TO MEMBERS The National Register of Scientific and Technical Personnel . • • . • . • . 2 77 The Employment Register ....••.••.•.•...•.•.•.•.•..••....• 277 The Combined Membership List, 1962-1963 •...•.....•.....•...•. 277 Corporate Members •.••...............•.•....•.....•••..• 278 The Australian Mathematical Society . 278 Backlog of Mathematical Research Journals • . • . • . • . 279 SUPPLEMENTARY PROGRAM - NO. 12 . • . 280 ABSTRACTS OF CONTRIBUTED PAPERS ...•.............••.....•.• 284 INDEX TO ADVERTISERS ...•...•..•..•.....•.....•............ 355 RESERVATION FORM . • • . • . • . • . • . • . • . 3 55 MEETINGS CALENDAR OF MEETINGS NOTE: This Calendar lists all of the meetings which have been approved by the Council up to the date at which this issue of the NOTICES was sent to press. The summer and annual meetings -
Group Actions on Dendrites and Curves 3
GROUP ACTIONS ON DENDRITES AND CURVES BRUNO DUCHESNE AND NICOLAS MONOD ABSTRACT. We establish obstructions for groups to act by homeomorphisms on dendrites. For instance, lattices in higher rank simple Lie groups will always fix a point or a pair. The same holds for irreducible lattices in products of connected groups. Further results include a Tits alternative and a description of the topological dynamics. We briefly discuss to what extent our results hold for more general topological curves. 1. INTRODUCTION 1.A — Dendrites. Recall that a dendrite is a locally connected continuum without simple closed curves. Other equivalent definitions and some basic facts are recalled in Section 2 below. A simple example of a dendrite is obtained by compactifying a countable simplicial tree (Section 12), but the typical dendrite is much more complicated: certain Julia sets are den- drites [BT07] and Wazewski’s˙ universal dendrite [Waz23a]˙ can be identified with the Berkovich projective line over Cp [HLP14]. The homeomorphisms group of some dendrites is enor- mous (Section 12), whilst for others it is trivial [dGW58, p. 443]. In fact, it was recognized early on [Why28, Why30] that any continuum has a canoni- cal dendrite quotient reflecting its cut-point structure, see [Bow98], [PS06] for the general statement. Bowditch made remarkable use of this quotient [Bow99b], leading to the solu- tion of the cut-point conjecture for hyperbolic groups [Bow99a, Swa96]. In this application, Bowditch’s dendrites retained a decidedly geometric aspect inherited from the hyperbolic group, namely the dynamical convergence property, allowing him to reconstruct a metric tree with an isometric action. -
From Schouten to Mackenzie: Notes on Brackets
From Schouten to Mackenzie: notes on brackets∗ Yvette Kosmann-Schwarzbach In Memory of Kirill Mackenzie (1951–2020) Abstract In this paper, dedicated to the memory of Kirill Mackenzie, I relate the origins and early development of the theory of graded Lie brackets, first in the pu- blications on differential geometry of Schouten, Nijenhuis, and Fr¨olicher–Nijenhuis, then in the work of Gerstenhaber and Nijenhuis–Richardson in cohomology theory. Keywords: graded Lie algebra, Schouten bracket, Nijenhuis torsion, Fr¨olicher– Nijenhuis bracket, Nijenhuis–Richardson bracket, Gerstenhaber algebra, Macken- zie theory. Introduction Many aspects of the contributions of Kirill Mackenzie to the theory of Lie groupoids and Lie algebroids, in particular to that of the double and multiple structures, are already classical and often cited. As a tribute to his memory, arXiv:2105.14828v1 [math.HO] 31 May 2021 I shall survey the history of the emergence of some theories that were tools – among many others – in the development and description of his mathematics. In his General Theory of Lie Groupoids and Lie Algebroids, in 2005, Mackenzie inserted a section of “Notes” at the end of each chapter. Yet he ad- vised his readers that his notes were “not comprehensive historical surveys”. After the chapter “Cohomology and Schouten calculus for Lie algebroids”, he wrote: “The Schouten bracket of multivector fields on a manifold goes back to Schouten [1954] and Nijenhuis [1955]. The same alge- braic structures on the cohomology of associative algebras were introduced by Gerstenhaber [1963].” ∗To appear in the Journal of Geometric Mechanics, 2021. 1 I shall try to expand on these elements of a story, and survey some of the early developments in the theory of the various graded brackets that Mackenzie cited and used1. -
Connected Sum at Infinity and Cantrell-Stallings Hyperplane Unknotting
CONNECTED SUM AT INFINITY AND CANTRELL-STALLINGS HYPERPLANE UNKNOTTING JACK S. CALCUT, HENRY C. KING, AND LAURENT C. SIEBENMANN Dedicated to Ljudmila V. Keldysh and the members of her topology seminar on the occasion of the centenary of her birth.1 1. Introduction We give a general treatment of the somewhat unfamiliar operation on manifolds called connected sum at infinity or CSI for short. A driving ambition has been to make the geometry behind the well defi- nition and basic properties of CSI as clear and elementary as possible. CSI then yields a very natural and elementary proof of a remark- able theorem of J.C. Cantrell and J.R. Stallings [Can63, Sta65]. It as- serts unknotting of cat embeddings of Rm−1 in Rm with m 6= 3, for all three classical manifold categories: topological (= top), piecewise linear (= pl), and differentiable (= diff) — as defined for example in [KS77]. It is one of the few major theorems whose statement and proof can be the same for all three categories. We give it the acronym HLT, which is short for “Hyperplane Linearization Theorem” (see The- orem 6.1 plus 7.3). We pause to set out some common conventions that are explained in [KS77] and in many textbooks. By default, spaces will be assumed metrizable, and separable (i.e. having a countable basis of open sets). arXiv:1010.2707v1 [math.GT] 13 Oct 2010 Simplicial complexes will be unordered. A pl space (often called a polyhedron) has a maximal family of pl compatible triangulations by Date: September 17, 2008 (revised October 12, 2010). -
2015 Newsletter
2015 NEWSLETTER DEPARTMENT OF MATHEMATICS This newsletter is published annually for alumni & friends of Mathematics at the University of Washington 1 as an associate professor. In addition to his outstanding research and teaching, Jayadev founded and ran the Illinois Geometry Lab, which brought faculty and graduate students together with undergraduates to As I approach the halfway point of my term as chair, I continue foster undergraduate research. In addition, it engaged to delight in the successes of our students and faculty. You community members across the state with activities will learn about these stories in the pages that follow. Let me from Urbana-Champaign to Chicago. Jayadev has preview some of them here. begun to establish a similar program—the Washington Experimental Mathematics Lab—here. I can’t wait to For the sixth year in a row and the twelfth year in the past see the results. fourteen, one of our math majors received the Dean’s Medal in the Natural Sciences. I imagined that our streak couldn’t Inevitably, in parallel with the arrival of the new continue, but that was before I received letters of support comes the departure of others. This year, we lost Albert for David Jekel from faculty in both Math and Classics, his Nijenhuis, a member of our faculty from 1956 to 1964 other major. I knew then that we had a winner, given that the before moving to the University of Pennsylvania, and Classics faculty were as in awe of David’s talents as our own. then an affiliate faculty member upon retirement, when He is now off to UCLA to continue his mathematical studies.