DOCSLIB.ORG

Volume 8 Number 4 October 1995

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Volume 8 Number 4 October 1995 VOLUME 8 NUMBER 4 OCTOBER 1995 AMERICANMATHEMATICALSOCIETY EDITORS William Fulton Benedict H. Gross Andrew Odlyzko Elias M. Stein Clifford Taubes ASSOCIATE EDITORS James G. Arthur Alexander Beilinson Louis Caffarelli Persi Diaconis Michael H. Freedman Joe Harris Dusa McDuff Hugh L. Montgomery Marina Ratner Richard Schoen Richard Stanley Gang Tian W. Hugh Woodin PROVIDENCE, RHODE ISLAND USA ISSN 0894-0347 Journal of the American Mathematical Society This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics. Subscription information. The Journal of the American Mathematical Society is pub- lished quarterly. Subscription prices for Volume 8 (1995) are $158 list, $126 institutional member, $95 individual member. Subscribers outside the United States and India must pay a postage surcharge of $8; subscribers in India must pay a postage surcharge of $18. Expedited delivery to destinations in North America $13; elsewhere $36. Back number information. For back issues see the AMS Catalog of Publications. Subscriptions and orders should be addressed to the American Mathematical Society, P. O. Box 5904, Boston, MA 02206-5904. All orders must be accompanied by payment. Other correspondence should be addressed to P. O. Box 6248, Providence, RI 02940- 6248. Copying and reprinting. Material in this journal may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledgment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Assistant Director of Production, American Mathematical Society, P. O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made bye-mail to reprint-permissionOmath.ams.org. Excluded from these provisions is material in articles for which the author holds copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand comer of the first page of each article.) The Journal ofthe American Mathematical Society is published quarterly by the Amer- ican Mathematical Society at 20 I Charles Street, Providence, RI 02904-2213 and is mailed from Providence, Rhode Island. Second class postage paid at Providence, Rhode Island. Postmaster: Send address changes to Journal of the AMS, American Mathemat- ical Society, P. O. Box 6248, Providence, RI02940-6248. © Copyright 1995 by the American Mathematical Society. All rights reserved. This journal is indexed in Science Citation Index ®, SciSearch ®, Research Alert ®, CompuMath Citation Index®, Current Contents®/Physical, Chemical & Earth Sciences. Printed in the United States of America. €) The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability. This publication was typeset using AMS-TEX, the American Mathematical Society's TEX macro system. to 9 8 7 6 5 4 3 2 00 99 98 INDEX TO VOLUME 8 1995 Baouendi, M. S. and Rothschild, Linda Preiss. Mappings of real algebraic hypersurfaces, 997 Bernstein, Joseph and Lunts, Valery. Localization for derived categories of(g, K)-modules, 819 Billey, Sara and Haiman, Mark. Schubert polynomials for the classical groups, 443 Bismut, Jean-Michel and Lott, John. Flat vector bundles, direct images· and higher real analytic torsion, 291 Bryant, Robert L. and Griffiths, Phillip A. Characteristic cohomology of differential systems (I): General theory, 507 Carbery, Anthony, Wainger, Stephen, and Wright, James. Hilbert transforms and maximal junc- tions associated to flat curves on the Heisenberg group, 141 Cattani, Eduardo, Deligne, Pierre, and Kaplan, Aroldo. On the locus ofHodge classes, 483 Charney, Ruth and Davis, Michael W. The K (n, 1 )-problem for hyperplane complements associated to infinite reflection groups, 597 Cogdell, J. W. and Piatetski-Shapiro, t I. On base change for odd orthogonal groups, 975 Cuntz, Joachim and Quillen, Daniel. Algebra extensions and nonsingularity, 251 __ . Cyclic homology and nonsingularity, 373 Davis, Michael W. See Charney, Ruth Deligne, Pierre. See Cattani, Eduardo Frenkel, Edward and Szenes, Andras. Crystal bases, dilogarithm identities, and torsion in algebraic K-theory, 629 Friedman, Robert. Vector bundles and SOC 3)-invariants for elliptic surfaces, 29 Glasner, Eli and Weiss, Benjamin. Quasi-factors of zero entropy systems, 665 Griffiths, Phillip A. See Bryant, Robert L. Grove, Karsten and Markvorsen, Steen. New extremal problems for the Riemannian recognition program via Alexandrov geometry, 1 Haiman, Mark. See Billey, Sara Judge, Christopher M. On the existence ofMaass cusp forms on hyperbolic surfaces with cone points, 715 Kahn, Jeff, Koml6s, Janos, and Szemeredi, Endre. On the probability that a random ±l-matrix is singular, 223 Kaplan, Aroldo. See Cattani, Eduardo Kollar, Janos. Nonrational hypersurfaces, 241 Koml6s, Janos. See Kahn, Jeff Kostant, Bertram. Immanant inequalities and O-weight spaces, 181 Levasseur, T. and Stafford, J. T. Invariant differential operators and an homomorphism ofHarish- Chandra, 365 Li, Peter and Tian, Gang. On the heat kernel of the Bergmann metric on algebraic varieties, 857 Lott, John. See Bismut, Jean-Michel Lunts, Valery. See Bernstein, Joseph Markvorsen, Steen. See Grove, Karsten Masuda, Mikiya and Petrie, Ted. Stably trivial equivariant algebraic vector bundles, 687 Minicozzi, William P., II. The Willmore junctional on lagrangian tori: Its relation to area and existence of smooth minimizers, 761 Parusinski, Adam and Pragacz, Piotr. Chern-Schwartz-Macpherson classes and the Euler charac- teristic ofdegeneracy loci and special divisors, 793 Petrie, Ted. See Masuda, Mikiya Piatetski-Shapiro, I. I. See Cogdell, J. W. Pragacz, Piotr. See Parusinski, Adam Quillen, Daniel. See Cuntz, Joachim ROdI, Vojtech and Rucinski, Andrzej. Threshold junctions for Ramsey properties, 917 INDEX TO VOLUME 8 Rothschild, Linda Preiss. See Baouendi, M. S. Ruciliski, Andrzej. See Rodl, Vojtech Smith, Hart F. and Soge, Christopher D. On the critical semilinear wave equation outside convex obstacles, 879 Soge, Christopher D. See Smith, Hart F. Stafford, J. T. See Levasseur, T. Stewart, C. L. and Top, J. On ranks oftwists ofelliptic curves and power-free values ofbinary forms, 943 Szemeredi, Endre. See Kahn, Jeff Szenes, Andras. See Frenkel, Edward Tian, Gang. See Li, Peter Top, J. See Stewart, C. L. Wainger, Stephen. See Carbery, Anthony Weiss, Benjamin. See Glasner, Eli Wright, James. See Carbery, Anthony Zhang, Shouwu. Positive line bundles on arithmetic varieties, 187 VOLUME P, 1995 AMERICAN MATHEMATICAL SOCIETY EDITORS William Fulton Benedict H. Gross Andrew Odlyzko Elias M. Stein Clifford Taubes ASSOCIATE EDITORS James G. Arthur Alexander Beilinson Louis Caffarelli Persi Diaconis Michael H. Freedman Joe Harris DusaMcDuff Hugh L. Montgomery Marina Ratner Richard Schoen Richard Stanley Gang Tian W. Hugh Woodin PROVIDENCE, RHODE ISLAND USA ISSN 0894-0347 .Journal of the American Mathematical Society This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics. Subscription information. The Journal of the American Mathematical Society is pub- lished quarterly. Subscription prices for Volume 8 (1995) are $1 58 list, $126 institutional member. $95 individual member. Subscribers outside the United States and India must pay a postage surcharge of $8; subscribers in India must pay a postage surcharge of $18. Expedited delivery to destinations in North America $13; elsewhere $36. Back number information. For back issues see the AMS Catalog of Publications. Subscriptions and orders should be addressed to the American Mathematical Society, P. O. Box 5904, Boston, MA 02206-5904. All orders must be accompanied by payment. Other correspondence should be addressed to P. O. Box 6248, Providence, RI 02940- ~~ . Copying and reprinting. Material in this journal may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledgment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Assistant Director of Production, American Mathematical Society, P. O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made bye-mail to reprint-permissionGmath.ams.org. Excluded from these provisions is material in articles for which the author holds copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand comer of the first page of each article.) The Journal ofthe American Mathematical Society is published quarterly by the Amer- ican Mathematical Society at 201 Charles Street, Providence, RI 02904-2213 and is mailed from Providence, Rhode Island. Second class postage paid at Providence, Rhode Island. Postmaster: Send address changes to Journal of the AMS, American Mathemat- ical Society,
Load more

Recommended publications
  • Sobolev Inequalities, Heat Kernels Under Ricci Flow, and The
    i \bookQiCRC-FM" | 2010/5/28 | 9:46 | page 2 | i i i Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincaré Conjecture i i i i i \bookQiCRC-FM" | 2010/5/28 | 9:46 | page 3 | i i i i i i i i \bookQiCRC-FM" | 2010/5/28 | 9:46 | page 4 | i i i Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincaré Conjecture Qi S. Zhang i i i i CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2010 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20140515 International Standard Book Number-13: 978-1-4398-3460-2 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit- ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers.
    [Show full text]
  • The Ricci Flow: Techniques and Applications Part IV: Long-Time Solutions and Related Topics
    Mathematical Surveys and Monographs Volume 206 The Ricci Flow: Techniques and Applications Part IV: Long-Time Solutions and Related Topics Bennett Chow Sun-Chin Chu David Glickenstein Christine Guenther James Isenberg Tom Ivey Dan Knopf Peng Lu Feng Luo Lei Ni American Mathematical Society The Ricci Flow: Techniques and Applications Part IV: Long-Time Solutions and Related Topics http://dx.doi.org/10.1090/surv/206 Mathematical Surveys and Monographs Volume 206 The Ricci Flow: Techniques and Applications Part IV: Long-Time Solutions and Related Topics Bennett Chow Sun-Chin Chu David Glickenstein Christine Guenther James Isenberg Tom Ivey Dan Knopf Peng Lu Feng Luo Lei Ni American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE Robert Guralnick Benjamin Sudakov Michael A. Singer, Chair Constantin Teleman MichaelI.Weinstein 2010 Mathematics Subject Classification. Primary 53C44, 53C21, 53C43, 58J35, 35K59, 35K05, 57Mxx, 57M50. For additional information and updates on this book, visit www.ams.org/bookpages/surv-206 Library of Congress Cataloging-in-Publication Data Chow, Bennett. The Ricci flow : techniques and applications / Bennett Chow... [et al.]. p. cm. — (Mathematical surveys and monographs, ISSN 0076-5376 ; v. 135) Includes bibliographical references and indexes. ISBN-13: 978-0-8218-3946-1 (pt. 1) ISBN-10: 0-8218-3946-2 (pt. 1) 1. Global differential geometry. 2. Ricci flow. 3. Riemannian manifolds. I. Title. QA670.R53 2007 516.362—dc22 2007275659 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research.
    [Show full text]
  • The Contributions of Stanley to the Fabric of Symmetric and Quasisymmetric Functions
    THE CONTRIBUTIONS OF STANLEY TO THE FABRIC OF SYMMETRIC AND QUASISYMMETRIC FUNCTIONS SARA C. BILLEY AND PETER R. W. MCNAMARA A E S A D I Dedicated to L N T C H R on the occasion of his 70th birthday. Y R Abstract. We weave together a tale of two rings, SYM and QSYM, following one gold thread spun by Richard Stanley. The lesson we learn from this tale is that \Combinatorial objects like to be counted by quasisymmetric functions." 1. Introduction The twentieth century was a remarkable era for the theory of symmetric func- tions. Schur expanded the range of applications far beyond roots of polynomials to the representation theory of GLn and Sn and beyond. Specht, Hall and Mac- donald unified the algebraic theory making it far more accessible. Lesieur recog- nized the connection between Schur functions and the topology of Grassmannian manifolds spurring interest and further developments by Borel, Bott, Bernstein{ Gelfand{Gelfand, Demazure and many others. Now, symmetric functions routinely appear in many aspects of mathematics and theoretical physics, and have significant importance in quantum computation. In that era of mathematical giants, Richard Stanley's contributions to symmet- ric functions are shining examples of how enumerative combinatorics has inspired and influenced some of the best work of the century. In this article, we focus on a few of the gems that continue to grow in importance over time. Specifically, we survey some results and applications for Stanley symmetric functions, chromatic symmetric functions, P -partitions, generalized Robinson{Schensted{Knuth corre- spondence, and flag symmetry of posets.
    [Show full text]
  • View Front and Back Matter from The
    VOLUME 19 NUMBER 4 OCTOBER 2006 J OOUF THE RNAL A M E R I C AN M A T H E M A T I C A L S O C I ET Y EDITORS Ingrid Daubechies Robert Lazarsfeld John W. Morgan Andrei Okounkov Terence Tao ASSOCIATE EDITORS Francis Bonahon Robert L. Bryant Weinan E Pavel I. Etingof Mark Goresky Alexander S. Kechris Robert Edward Kottwitz Peter Kronheimer Haynes R. Miller Andrew M. Odlyzko Bjorn Poonen Victor S. Reiner Oded Schramm Richard L. Taylor S. R. S. Varadhan Avi Wigderson Lai-Sang Young Shou-Wu Zhang PROVIDENCE, RHODE ISLAND USA ISSN 0894-0347 Available electronically at www.ams.org/jams/ Journal of the American Mathematical Society This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics. Submission information. See Information for Authors at the end of this issue. Publisher Item Identifier. The Publisher Item Identifier (PII) appears at the top of the first page of each article published in this journal. This alphanumeric string of characters uniquely identifies each article and can be used for future cataloging, searching, and electronic retrieval. Postings to the AMS website. Articles are posted to the AMS website individually after proof is returned from authors and before appearing in an issue. Subscription information. The Journal of the American Mathematical Society is published quarterly. Beginning January 1996 the Journal of the American Mathemati- cal Society is accessible from www.ams.org/journals/. Subscription prices for Volume 19 (2006) are as follows: for paper delivery, US$276 list, US$221 institutional member, US$248 corporate member, US$166 individual member; for electronic delivery, US$248 list, US$198 institutional member, US$223 corporate member, US$149 individual mem- ber.
    [Show full text]
  • Pure Mathematics
    Proceedings of Symposia in PURE MATHEMATICS Volume 101 Representations of Reductive Groups Conference in honor of Joseph Bernstein Representation Theory & Algebraic Geometry June 11–16, 2017 Weizmann Institute of Science, Rehovot, Israel and The Hebrew University of Jerusalem, Is- rael Avraham Aizenbud Dmitry Gourevitch David Kazhdan Erez M. Lapid Editors 10.1090/pspum/101 Volume 101 Representations of Reductive Groups Conference in honor of Joseph Bernstein Representation Theory & Algebraic Geometry June 11–16, 2017 Weizmann Institute of Science, Rehovot, Israel and The Hebrew University of Jerusalem, Is- rael Avraham Aizenbud Dmitry Gourevitch David Kazhdan Erez M. Lapid Editors Proceedings of Symposia in PURE MATHEMATICS Volume 101 Representations of Reductive Groups Conference in honor of Joseph Bernstein Representation Theory & Algebraic Geometry June 11–16, 2017 Weizmann Institute of Science, Rehovot, Israel and The Hebrew University of Jerusalem, Is- rael Avraham Aizenbud Dmitry Gourevitch David Kazhdan Erez M. Lapid Editors 2010 Mathematics Subject Classification. Primary 11F27, 11F70, 20C08, 20C33, 20G05, 20G20, 20G25, 22E47. Library of Congress Cataloging-in-Publication Data Names: Conference on Representation Theory and Algebraic Geometry in honor of Joseph Bern- stein (2017 : Jerusalem, Israel) | Aizenbud, Avraham, 1983- editor. | Gourevitch, Dmitry, 1981- editor. | Kazhdan, D. A. (David A.), 1946- editor. | Lapid, Erez, 1971- editor. | Bernstein, Joseph, 1945- honoree. Title: Representations of reductive groups : Conference on Representation Theory and Algebraic Geometry in honor of Joseph Bernstein, June 11-16, 2017, The Weizmann Institute of Sci- ence & The Hebrew University of Jerusalem, Jerusalem, Israel / Avraham Aizenbud, Dmitry Gourevitch, David Kazhdan, Erez M. Lapid, editors. Description: Providence, Rhode Island : American Mathematical Society, [2019] | Series: Pro- ceedings of symposia in pure mathematics ; Volume 101 | Includes bibliographical references.
    [Show full text]
  • Arxiv:1801.07636V1 [Math.DG]
    ON CALABI’S EXTREMAL METRICS AND PROPERNESS WEIYONG HE Abstract. In this paper we extend recent breakthrough of Chen-Cheng [11, 12, 13] on ex- istence of constant scalar K¨ahler metric on a compact K¨ahler manifold to Calabi’s extremal metric. Our argument follows [13] and there are no new a prior estimates needed, but rather there are necessary modifications adapted to the extremal case. We prove that there exists an extremal metric with extremal vector V if and only if the modified Mabuchi energy is proper, modulo the action the subgroup in the identity component of automorphism group which commutes with the flow of V . We introduce two essentially equivalent notions, called reductive properness and reduced properness. We observe that one can test reductive proper- ness/reduced properness only for invariant metrics. We prove that existence of an extremal metric is equivalent to reductive properness/reduced properness of the modified Mabuchi en- ergy. 1. Introduction Recently Chen and Cheng [11, 12, 13] have made surprising breakthrough in the study of constant scalar curvature (csck) on a compact K¨ahler manifold (M, [ω], J), with a fixed K¨ahler class [ω]. A K¨ahler metric with constant scalar curvature are special cases of Calabi’s extremal metric [6, 7], which was introduced by E. Calabi in 1980s to find a canonical representative within the K¨ahler class [ω]. In [21], S. K. Donaldson proposed a beautiful program in K¨ahler geometry to attack Calabi’s renowned problem of existence of csck metrics in terms of the geometry of space of K¨ahler potentials with the Mabuchi metric [39], H := φ C∞(M) : ωφ = ω + √ 1∂∂φ¯ > 0 .
    [Show full text]
  • VTC2011-Spring Final Program
    The 73rd IEEE Vehicular Technology Conference Final Programme 15 - 18 May 2011 Budapest, Hungary Welcome from the General Chair Dear Colleagues, Allow me to commence by welcoming you to VTC It is my privilege to convey the community's 2011 Spring in the vibrant city of Budapest! I have gratitude to the conference patrons, namely to been faithfully attending VTC for the past two Ericsson, Huawei Technologies, HTE and Wiley- decades and I have a vivid recollection of this Blackwell. Needless to say that a lot of further dynamic period of spectacular growth across the volunteers contributed in numerous ways to the wireless communications industry. success of the conference. My hope is that you would enjoy the rich technical On a technical note, the advances of the past three blend of plenaries and panels presented by decades facilitated a 1000-fold throughput distinguished industrial and academic leaders improvement, but naturally, this was achieved at converging on Budapest from all over the globe. the cost of a substantially increased power These will also be complemented by tutorials, consumption. In the light of the escalating energy workshops and the regular technical sessions. prices this motivated the design of ‘green radios’, aiming for more power-efficient solutions – all in I am indebted to the entire organizing and technical all, an exciting era for our community. program committee, especially to the TPC Co- Chairs Drs Andrea Conti, Iain Collings and Wei My hope is that you, dear Colleague will enjoy the Chen for their generous support as well as to all the technical discussions, meeting old friends and Track Chairs for their dedication.
    [Show full text]
  • An Interview with Martin Davis
    Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Geometry Ramanujan‘s Lost Notebook An Introduction to Mathematical of the American Mathematical Society Selected Topics in Plane and Solid Part II Cryptography May 2008 Volume 55, Number 5 Geometry G. E. Andrews, Penn State University, University J. Hoffstein, J. Pipher, J. Silverman, Brown J. Aarts, Delft University of Technology, Park, PA, USA; B. C. Berndt, University of Illinois University, Providence, RI, USA Mediamatics, The Netherlands at Urbana, IL, USA This self-contained introduction to modern This is a book on Euclidean geometry that covers The “lost notebook” contains considerable cryptography emphasizes the mathematics the standard material in a completely new way, material on mock theta functions—undoubtedly behind the theory of public key cryptosystems while also introducing a number of new topics emanating from the last year of Ramanujan’s life. and digital signature schemes. The book focuses Interview with Martin Davis that would be suitable as a junior-senior level It should be emphasized that the material on on these key topics while developing the undergraduate textbook. The author does not mock theta functions is perhaps Ramanujan’s mathematical tools needed for the construction page 560 begin in the traditional manner with abstract deepest work more than half of the material in and security analysis of diverse cryptosystems. geometric axioms. Instead, he assumes the real the book is on q- series, including mock theta Only basic linear algebra is required of the numbers, and begins his treatment by functions; the remaining part deals with theta reader; techniques from algebra, number theory, introducing such modern concepts as a metric function identities, modular equations, and probability are introduced and developed as space, vector space notation, and groups, and incomplete elliptic integrals of the first kind and required.
    [Show full text]
  • A Bijective Proof of Macdonald's Reduced Word Formula
    FPSAC 2016 Vancouver, Canada DMTCS proc. BC, 2016, 251–262 A bijective proof of Macdonald’s reduced word formula Sara C. Billey1y, Alexander E. Holroyd2z, and Benjamin J. Young2x 1Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA 2Microsoft Research, 1 Microsoft Way, Redmond, WA 98052, USA 3Department of Mathematics, 1222 University of Oregon, Eugene, OR 97403 Abstract. We describe a bijective proof of Macdonald’s reduced word identity using pipe dreams and Little’s bumping algorithm. The proof extends to a principal specialization of the identity due to Fomin and Stanley. Our bijective tools also allow us to address a problem posed by Fomin and Kirillov from 1997, using work of Wachs, Lenart and Serrano- Stump. Resum´ e.´ Nous donnons une preuve bijective de l’identite´ des mots reduits´ de Macdonald, en utilisant des “pipe dreams” et l’algorithme “bumping” de Little. La preuve est etendue´ a` une specialisation´ principale de l’identite´ due a` Fomin et Stanley. La methode´ bijective nous permet aussi de traiter un probleme` pose´ par Fomin et Kirillov en 1997, en utilisant les travaux de Wachs, Lenart et Serrano-Stump. Keywords. reduced words, Schubert polynomials, RC graphs, pipe dreams, bijective proof, algorithmic bijection 1 Introduction Macdonald gave a remarkable formula connecting a weighted sum of reduced words for permutations with the number of terms in a Schubert polynomial Sπ(x1; : : : ; xn). For a permutation π 2 Sn, let `(π) be its inversion number and let R(π) denote the set of its reduced words. (See Section 2 for definitions.) Theorem 1.1 (Macdonald [Mac91, (6.11)]) Given a permutation π 2 Sn with `(π) = p, one has X a1 · a2 ··· ap = p! Sπ(1;:::; 1): (1.1) (a1;a2;:::;ap)2R(π) For example, the permutation [3; 2; 1] 2 S3 has 2 reduced words, R([3; 2; 1]) = f(1; 2; 1); (2; 1; 2)g.
    [Show full text]
  • Canonical Metric on a Mildly Singular Kähler Varieties with an Intermediate Log Kodaira Dimension Hassan Jolany
    Canonical metric on a mildly singular Kähler varieties with an intermediate log Kodaira dimension Hassan Jolany To cite this version: Hassan Jolany. Canonical metric on a mildly singular Kähler varieties with an intermediate log Kodaira dimension. 2017. hal-01413751v2 HAL Id: hal-01413751 https://hal.archives-ouvertes.fr/hal-01413751v2 Preprint submitted on 21 Jun 2017 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. Canonical metric on a mildly singular Kahler¨ varieties with an intermediate log Kodaira dimension HASSAN JOLANY Existence of canonical metric on a canonical model of projective singular variety was a long standing conjecture and the major part of this conjecture is about varieties which do not have definite first Chern class(most of the varieties do not have definite first Chern class). There is a program which is known as Song-Tian program for finding canonical metric on canonical model of a projective variety by using Minimal Model Program. In this paper, we apply Song-Tian program for mildly singular pair (X; D) via Log Minimal Model Program where D is a simple normal crossing divisor on X with conic singularities.
    [Show full text]
  • Characters of Representations of Affine Kac-Moody Lie Algebras at The
    CHARACTERS OF REPRESENTATIONS OF AFFINE KAC-MOODY LIE ALGEBRAS AT THE CRITICAL LEVEL TOMOYUKI ARAKAWA 1. Introduction and Main Results 1.1. Let g¯ be a complex simple Lie algebra of rank l, g non-twisted affine Kac- Moody Lie algebra associated with g¯: (1) g = g¯⊗C[t,t−1] ⊕ CK ⊕ CD. The commutation relations of g are given by the following. [X(m), Y (n)] = [X, Y ](m + n)+ mδm+n,0(X|Y )K, [D,X(m)] = mX(m), [K, g]=0 for X, Y ∈ g¯, m,n ∈ Z, where X(m) = X⊗tm with X ∈ g¯ and m ∈ Z and (·|·) is the normalized invariant inner product of g¯. We identify g¯ with g¯⊗C ⊂ g. Fix the triangular decomposition g¯ = n¯− ⊕ h¯ ⊕ n¯+, and the Cartan subalgebra of g as ∗ ∗ h = h¯ ⊕ CK ⊕ CD. We have h = h¯ ⊕ CΛ0 ⊕ Cδ, where Λ0 and δ are elements dual to K and D, respectively. Let L(λ) be the irreducible highest weight representation of g of highest weight ∗ λ ∈ h with respect to the standard triangular decomposition g = n− ⊕ h ⊕ n+, where −1 −1 n− = n¯− ⊕ g¯⊗C[t ]t , n+ = n¯+ ⊕ g¯⊗C[t]t. The central element K acts on L(λ) as the multiplication by the constant hλ, Ki, which is called the level of L(λ). The level hλ, Ki = −h∨ is called critical, where h∨ is the dual Coxeter number of g¯. 1.2. Let ch L(λ) be the formal character of L(λ): µ µ ch L(λ)= e dimC L(λ) , arXiv:0706.1817v2 [math.QA] 15 Jun 2007 µ h∗ X∈ where L(λ)µ is the weight space of L(λ) of weight µ.
    [Show full text]
  • Prizes and Awards
    SAN DIEGO • JAN 10–13, 2018 January 2018 SAN DIEGO • JAN 10–13, 2018 Prizes and Awards 4:25 p.m., Thursday, January 11, 2018 66 PAGES | SPINE: 1/8" PROGRAM OPENING REMARKS Deanna Haunsperger, Mathematical Association of America GEORGE DAVID BIRKHOFF PRIZE IN APPLIED MATHEMATICS American Mathematical Society Society for Industrial and Applied Mathematics BERTRAND RUSSELL PRIZE OF THE AMS American Mathematical Society ULF GRENANDER PRIZE IN STOCHASTIC THEORY AND MODELING American Mathematical Society CHEVALLEY PRIZE IN LIE THEORY American Mathematical Society ALBERT LEON WHITEMAN MEMORIAL PRIZE American Mathematical Society FRANK NELSON COLE PRIZE IN ALGEBRA American Mathematical Society LEVI L. CONANT PRIZE American Mathematical Society AWARD FOR DISTINGUISHED PUBLIC SERVICE American Mathematical Society LEROY P. STEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH American Mathematical Society LEROY P. STEELE PRIZE FOR MATHEMATICAL EXPOSITION American Mathematical Society LEROY P. STEELE PRIZE FOR LIFETIME ACHIEVEMENT American Mathematical Society SADOSKY RESEARCH PRIZE IN ANALYSIS Association for Women in Mathematics LOUISE HAY AWARD FOR CONTRIBUTION TO MATHEMATICS EDUCATION Association for Women in Mathematics M. GWENETH HUMPHREYS AWARD FOR MENTORSHIP OF UNDERGRADUATE WOMEN IN MATHEMATICS Association for Women in Mathematics MICROSOFT RESEARCH PRIZE IN ALGEBRA AND NUMBER THEORY Association for Women in Mathematics COMMUNICATIONS AWARD Joint Policy Board for Mathematics FRANK AND BRENNIE MORGAN PRIZE FOR OUTSTANDING RESEARCH IN MATHEMATICS BY AN UNDERGRADUATE STUDENT American Mathematical Society Mathematical Association of America Society for Industrial and Applied Mathematics BECKENBACH BOOK PRIZE Mathematical Association of America CHAUVENET PRIZE Mathematical Association of America EULER BOOK PRIZE Mathematical Association of America THE DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY TEACHING OF MATHEMATICS Mathematical Association of America YUEH-GIN GUNG AND DR.CHARLES Y.
    [Show full text]