Biographies of Candidates 1995
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Conference Celebrating the 70Th Birthday of Prof. Krzysztof M. Pawa Lowski 11–13 January 2021, Online Conference Via Zoom
kpa70 Conference celebrating the 70th birthday of Prof. Krzysztof M. Pawa lowski 11{13 January 2021, Online conference via Zoom https://kpa70.wmi.amu.edu.pl/ Invited Speakers: • William Browder (Princeton University), • Sylvain Cappell (New York University), • James F. Davis (Indiana University Bloomington), • Bogus law Hajduk (University of Warmia and Mazury), • Jaros law K¸edra(University of Aberdeen), • Mikiya Masuda (Osaka City University), • Masaharu Morimoto (Okayama University), • Robert Oliver (Paris University 13), • Taras Panov (Moscow State University), • J´ozefPrzytycki (George Washington University and University of Gda´nsk), • Toshio Sumi (Kyushu University). Organizers: • Marek Kaluba, • Wojciech Politarczyk, • Bartosz Biadasiewicz, • Lukasz Michalak, • Piotr Mizerka, • Agnieszka Stelmaszyk-Smierzchalska.´ i Monday, January 11 Time Washington Warsaw Tokyo 6:45 { 12:45 { 20:45 { Opening 7:00 13:00 21:00 Mikiya Masuda, 7:00 { 13:00 { 21:00 { Invariants of the cohomology rings of the permutohedral 7:45 13:45 21:45 varieties Taras Panov, 8:00 { 14:00 { 22:00 { Holomorphic foliations and complex moment-angle 8:45 14:45 22:45 manifolds 9:15 { 15:15 { 23:15 { Robert Oliver, 10:00 16:00 00:00 The loop space homology of a small category J´ozefH. Przytycki, 10:15 { 16:15 { 00:15 { Adventures of Knot Theorist: 11:00 17:00 01:00 from Fox 3-colorings to Yang-Baxter homology{ 5 years after Pozna´ntalks Tuesday, January 12 Time Washington Warsaw Tokyo Piotr Mizerka, 6:20 { 12:20 { 20:20 { New results on one and two fixed point actions 6:45 12:45 20:45 on spheres 7:00 { 13:00 { 21:00 { Masaharu Morimoto, 7:45 13:45 21:45 Equivariant Surgery and Dimension Conditions 8:00 { 14:00 { 22:00 { Toshio Sumi, 8:45 14:45 22:45 Smith Problem and Laitinen's Conjecture Sylvain Cappell, 9:15 { 15:15 { 23:15 { Fixed points of G-CW-complex with prescribed 10:00 16:00 00:00 homotopy type 10:15 { 16:15 { 00:15 { James F. -
Prospects in Topology
Annals of Mathematics Studies Number 138 Prospects in Topology PROCEEDINGS OF A CONFERENCE IN HONOR OF WILLIAM BROWDER edited by Frank Quinn PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY 1995 Copyright © 1995 by Princeton University Press ALL RIGHTS RESERVED The Annals of Mathematics Studies are edited by Luis A. Caffarelli, John N. Mather, and Elias M. Stein Princeton University Press books are printed on acid-free paper and meet the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources Printed in the United States of America by Princeton Academic Press 10 987654321 Library of Congress Cataloging-in-Publication Data Prospects in topology : proceedings of a conference in honor of W illiam Browder / Edited by Frank Quinn. p. cm. — (Annals of mathematics studies ; no. 138) Conference held Mar. 1994, at Princeton University. Includes bibliographical references. ISB N 0-691-02729-3 (alk. paper). — ISBN 0-691-02728-5 (pbk. : alk. paper) 1. Topology— Congresses. I. Browder, William. II. Quinn, F. (Frank), 1946- . III. Series. QA611.A1P76 1996 514— dc20 95-25751 The publisher would like to acknowledge the editor of this volume for providing the camera-ready copy from which this book was printed PROSPECTS IN TOPOLOGY F r a n k Q u in n , E d it o r Proceedings of a conference in honor of William Browder Princeton, March 1994 Contents Foreword..........................................................................................................vii Program of the conference ................................................................................ix Mathematical descendants of William Browder...............................................xi A. Adem and R. J. Milgram, The mod 2 cohomology rings of rank 3 simple groups are Cohen-Macaulay........................................................................3 A. -
Bounds of the Mertens Functions
Advances in Dynamical Systems and Applications. ISSN 0973-5321, Volume 16, Number 1, (2021) pp. 35-44 © Research India Publications https://dx.doi.org/10.37622/ADSA/16.1.2021.35-44 Bounds of the Mertens Functions Darrell Coxa, Sourangshu Ghoshb, Eldar Sultanowc aGrayson County College, Denison, TX 75020, USA bDepartment of Civil Engineering , Indian Institute of Technology Kharagpur, West Bengal, India cPotsdam University, 14482 Potsdam, Germany Abstract In this paper we derive new properties of Mertens function and discuss about a likely upper bound of the absolute value of the Mertens function √log(푥!) > |푀(푥)| when 푥 > 1. Using this likely bound we show that we have a sufficient condition to prove the Riemann Hypothesis. 1. INTRODUCTION We define the Mobius Function 휇(푘). Depending on the factorization of n into prime factors the function can take various values in {−1, 0, 1} 휇(푛) = 1 if n has even number of prime factors and it is also square- free(divisible by no perfect square other than 1) 휇(푛) = −1 if n has odd number of prime factors and it is also square-free 휇(푛) = 0 if n is divisible by a perfect square. 푛 Mertens function is defined as 푀(푛) = ∑푘=1 휇(푘) where 휇(푘) is the Mobius function. It can be restated as the difference in the number of square-free integers up to 푥 that have even number of prime factors and the number of square-free integers up to 푥 that have odd number of prime factors. The Mertens function rather grows very slowly since the Mobius function takes only the value 0, ±1 in both the positive and 36 Darrell Cox, Sourangshu Ghosh, Eldar Sultanow negative directions and keeps oscillating in a chaotic manner. -
Topology MATH-GA 2310 and MATH-GA 2320
Topology MATH-GA 2310 and MATH-GA 2320 Sylvain Cappell Transcribed by Patrick Lin Figures transcribed by Ben Kraines Abstract. These notes are from a two-semester introductory sequence in Topology at the graduate level, as offered in the Fall 2013{Spring 2014 school year at the Courant Institute of Mathematical Sciences, a school of New York University. The primary lecturer for the course was Sylvain Cappell. Three lectures were given by Edward Miller during the Fall semester. Course Topics: Point-Set Topology (Metric spaces, Topological spaces). Homotopy (Fundamental Group, Covering Spaces). Manifolds (Smooth Maps, Degree of Maps). Homology (Cellular, Simplicial, Singular, Axiomatic) with Applications, Cohomology. Parts I and II were covered in MATH-GA 2310 Topology I; and Parts III and IV were covered in MATH-GA 2320 Topology II. The notes were transcribed live (with minor modifications) in LATEX by Patrick Lin. Ben Kraines provided the diagrams from his notes for the course. These notes are in a draft state, and thus there are likely many errors and inconsistencies. These are corrected as they are found. Revision: 21 Apr 2016 15:29. Contents Chapter 0. Introduction 1 Part I. Point-Set Topology 5 Chapter 1. Topological Spaces 7 1.1. Sets and Functions 7 1.2. Topological Spaces 8 1.3. Metric Spaces 8 1.4. Constructing Topologies from Existing Ones 9 Chapter 2. Properties of Topological Spaces 13 2.1. Continuity and Compactness 13 2.2. Hausdorff Spaces 15 2.3. Connectedness 15 Part II. The Fundamental Group 17 Chapter 3. Basic Notions of Homotopy 19 3.1. -
NUMBER THEORY and COMBINATORICS SEMINAR UNIVERSITY of LETHBRIDGE Contents
PAST SPEAKERS IN THE NUMBER THEORY AND COMBINATORICS SEMINAR OF THE DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE AT THE UNIVERSITY OF LETHBRIDGE http://www.cs.uleth.ca/~nathanng/ntcoseminar/ Organizers: Nathan Ng and Dave Witte Morris (starting Fall 2011) Amir Akbary (Fall 2007 – Fall 2010) Contents ........................... Fall 2020 2 Spring 2014 ....................... 48 ........................ Spring 2020 5 Fall 2013 .......................... 52 ........................... Fall 2019 9 Spring 2013 ....................... 55 ....................... Spring 2019 12 Fall 2012 .......................... 59 .......................... Fall 2018 16 Spring 2012 ....................... 63 ....................... Spring 2018 20 Fall 2011 .......................... 67 .......................... Fall 2017 24 Fall 2010 .......................... 70 ....................... Spring 2017 28 Spring 2010 ....................... 71 .......................... Fall 2016 31 Fall 2009 .......................... 73 ....................... Spring 2016 34 Spring 2009 ....................... 75 .......................... Fall 2015 39 Fall 2008 .......................... 77 ....................... Spring 2015 42 Spring 2008 ....................... 80 .......................... Fall 2014 45 Fall 2007 .......................... 83 Fall 2020 Open problem session Sep 28, 2020 Please bring your favourite (math) problems. Anyone with a problem to share will be given about 5 minutes to present it. We will also choose most of the speakers for the rest of the semester. -
The Riemann Hypothesis Is Not True Jonathan Sondow, Cristian Dumitrescu, Marek Wolf
The Riemann Hypothesis is not true Jonathan Sondow, Cristian Dumitrescu, Marek Wolf To cite this version: Jonathan Sondow, Cristian Dumitrescu, Marek Wolf. The Riemann Hypothesis is not true. 2021. hal-03135456v2 HAL Id: hal-03135456 https://hal.archives-ouvertes.fr/hal-03135456v2 Preprint submitted on 3 May 2021 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. The Riemann Hypothesis is most likely not true J:Sondow1 , C. Dumitrescu2, M. Wolf 3 1https://jonathansondow.github.io 2e-mail: [email protected] 3e-mail: [email protected] Abstract We show that there is a possible contradiction between the Riemann's Hypothesis and the theorem on the strong universality of the zeta func- tion. 1 Introduction In his only paper devoted to the number theory published in 1859 [32] (it was also included as an appendix in [12]) Bernhard Riemann continued analytically the series 1 X 1 ; s = σ + it; σ > 1 (1) ns n=1 to the complex plane with exception of s = 1, where the above series is a harmonic divergent series. He has done it using the integral Γ(1 − s) Z (−z)s dz ζ(s) = z ; (2) 2πi C e − 1 z where the contour C is 6 C ' - - & The definition of (−z)s is (−z)s = es log(−z), where the definition of log(−z) conforms to the usual definition of log(z) for z not on the negative real axis as the branch which is real for positive real z, thus (−z)s is not defined on the positive real axis, 1 see [12, p.10]. -
Stratified Spaces: Joining Analysis, Topology and Geometry
Mathematisches Forschungsinstitut Oberwolfach Report No. 56/2011 DOI: 10.4171/OWR/2011/56 Stratified Spaces: Joining Analysis, Topology and Geometry Organised by Markus Banagl, Heidelberg Ulrich Bunke, Regensburg Shmuel Weinberger, Chicago December 11th – December 17th, 2011 Abstract. For manifolds, topological properties such as Poincar´eduality and invariants such as the signature and characteristic classes, results and techniques from complex algebraic geometry such as the Hirzebruch-Riemann- Roch theorem, and results from global analysis such as the Atiyah-Singer in- dex theorem, worked hand in hand in the past to weave a tight web of knowl- edge. Individually, many of the above results are in the meantime available for singular stratified spaces as well. The 2011 Oberwolfach workshop “Strat- ified Spaces: Joining Analysis, Topology and Geometry” discussed these with the specific aim of cross-fertilization in the three contributing fields. Mathematics Subject Classification (2000): 57N80, 58A35, 32S60, 55N33, 57R20. Introduction by the Organisers The workshop Stratified Spaces: Joining Analysis, Topology and Geometry, or- ganised by Markus Banagl (Heidelberg), Ulrich Bunke (Regensburg) and Shmuel Weinberger (Chicago) was held December 11th – 17th, 2011. It had three main components: 1) Three special introductory lectures by Jonathan Woolf (Liver- pool), Shoji Yokura (Kagoshima) and Eric Leichtnam (Paris); 2) 20 research talks, each 60 minutes; and 3) a problem session, led by Shmuel Weinberger. In total, this international meeting was attended by 45 participants from Canada, China, England, France, Germany, Italy, Japan, the Netherlands, Spain and the USA. The “Oberwolfach Leibniz Graduate Students” grants enabled five advanced doctoral students from Germany and the USA to attend the meeting. -
A Solution to the Riemann Hypothesis
A solution to the Riemann Hypothesis Jeet Kumar Gaur PhD in Mechanical Eng. Dept. Indian Institute of Science, Bangalore, India email id: [email protected] July 2, 2021 Abstract This paper discloses a proof for the Riemann Hypothesis. On iterative expansion of the integration term in functional equation of Riemann zeta function we get a series. At the ‘non- trivial’ zeros of zeta function, value of the series is zero. Thus, Riemann hypothesis is false if that happens for an ‘s’ off the critical line(<(s) = 1=2). This series has two components. These components are such that if one component is defined as f(s) the other equals f(1 − s). For the hypothesis to be false one component is additive inverse of the other. From geometric analysis of component series function f(s) we find that f(s) 6= 0 anywhere in the critical strip. Further, using the additive properties of odd functions we prove by contradiction that they cannot be each other’s additive inverse for any s, off the critical line. Thus, proving truth of the hypothesis. 1 Introduction The Riemann Hypothesis has become one of the most centralized problems in mathematics today. It has to do with the position of ‘non-trivial’ zeros of the zeta function that encrypt information about prime numbers. The hypothesis has its roots predominantly in number theory. However, over time the ways to approach the problem have diversified with new evidence suggesting connections with seemingly unrelated fields like random matrices, chaos theory and quantum arXiv:2103.02223v3 [math.GM] 30 Jun 2021 physics [1][2]. -
The Courant Institute of Mathematical Sciences: 75 Years of Excellence by M.L
Celebrating 75 Years The Courant Institute of Mathematical Sciences at New York University Subhash Khot wins NSF’s Alan T. Waterman Award This award is given annually by the NSF to a single outstanding young researcher in any of the fields of science, engineering, and social science it supports. Subhash joins a very distinguished recipient list; few mathematicians or computer scientists have won this award in the past. Subhash has made fundamental contributions to the understanding of the exact difficulty of optimization problems arising in industry, mathematics and science. His work has created a paradigm which unites a broad range of previously disparate optimization problems and connects them to other fields of study including geometry, coding, learning and more. For the past four decades, complexity theory has relied heavily on the concept of NP-completeness. In 2002, Subhash proposed the Unique Games Conjecture (UGC). This postulates that the task of finding a “good” approximate solution for a variant Spring / Summer 2010 7, No. 2 Volume of the standard NP-complete constraint satisfaction problem is itself NP-complete. What is remarkable is that since then the UGC has Photo: Gayatri Ratnaparkhi proven to be a core postulate for the dividing line In this Issue: between approximability and inapproximability in numerous problems of diverse nature, exactly specifying the limit of efficient approximation for these problems, and thereby establishing UGC as an important new paradigm in complexity theory. As a further Subhash Khot wins NSF’s Alan T. Waterman Award 1 bonus, UGC has inspired many new techniques and results which are valid irrespective of UGC’s truth. -
1 Mathematical Savoir Vivre
STANDARD,EXCEPTION,PATHOLOGY JERZY POGONOWSKI Department of Applied Logic Adam Mickiewicz University www.logic.amu.edu.pl [email protected] ABSTRACT. We discuss the meanings of the concepts: standard, excep- tion and pathology in mathematics. We take into account some prag- matic components of these meanings. Thus, standard and exceptional objects obtain their status from the point of view of an underlying the- ory and its applications. Pathological objects differ from exceptional ones – the latter may e.g. form a collection beyond some established classification while the former are in a sense unexpected or unwilling, according to some intuitive beliefs shared by mathematicians of the gi- ven epoch. Standard and pathology are – to a certain extent – flexible in the development of mathematical theories. Pathological objects may become „domesticated” and give rise to new mathematical domains. We add a few comments about the dynamics of mathematical intuition and the role of extremal axioms in the search of intended models of mathematical theories. 1 Mathematical savoir vivre Contrary to that what a reader might expect from the title of this section we are not going to discuss the behavior of mathematicians themselves. Rather, we devote our attention to the following phrase which is very common in mathematical texts: An object X is well behaving. Here X may stand for a function, a topological space, an algebraic structure, etc. It should be overtly stressed that well behaving of mathematical objects is al- ways related to some investigated theory or its applications. There is nothing like absolute well behavior – properties of objects are evaluated from a pragmatic point of view. -
The Mertens Conjecture
The Mertens conjecture Herman J.J. te Riele∗ Title of c Higher Education Press This book April 8, 2015 and International Press ALM ??, pp. ?–? Beijing-Boston Abstract The Mertens conjecture states that |M(x)|x−1/2 < 1 for x > 1, where M(x) = P1≤n≤x µ(n) and where µ(n) is the M¨obius function defined by: µ(1) = 1, µ(n) = (−1)k if n is the product of k distinct primes, and µ(n)=0 if n is divisible by a square > 1. The truth of the Mertens conjecture implies the truth of the Riemann hypothesis and the simplicity of the complex zeros of the Riemann zeta function. This paper gives a concise survey of the history and state-of-affairs concerning the Mertens conjecture. Serious doubts concerning this conjecture were raised by Ingham in 1942 [12]. In 1985, the Mertens conjecture was disproved by Odlyzko and Te Riele [23] by making use of the lattice basis reduction algorithm of Lenstra, Lenstra and Lov´asz [19]. The best known results today are that |M(x)|x−1/2 ≥ 1.6383 and there exists an x< exp(1.004 × 1033) for which |M(x)|x−1/2 > 1.0088. 2000 Mathematics Subject Classification: Primary 11-04, 11A15, 11M26, 11Y11, 11Y35 Keywords and Phrases: Mertens conjecture, Riemann hypothesis, zeros of the Riemann zeta function 1 Introduction Let µ(n) be the M¨obius function with values µ(1) = 1, µ(n) = ( 1)k if n is the product of k distinct primes, and µ(n) = 0 if n is divisible by a square− > 1. -
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.