August 2019 Table of Contents
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The Association for Women in Mathematics: How and Why It Was
Mathematical Communities t’s 2011 and the Association for Women in Mathematics The Association (AWM) is celebrating 40 years of supporting and II promoting female students, teachers, and researchers. It’s a joyous occasion filled with good food, warm for Women conversation, and great mathematics—four plenary lectures and eighteen special sessions. There’s even a song for the conference, titled ‘‘((3 + 1) 9 3 + 1) 9 3 + 1 Anniversary in Mathematics: How of the AWM’’ and sung (robustly!) to the tune of ‘‘This Land is Your Land’’ [ICERM 2011]. The spirit of community and and Why It Was the beautiful mathematics on display during ‘‘40 Years and Counting: AWM’s Celebration of Women in Mathematics’’ are truly a triumph for the organization and for women in Founded, and Why mathematics. It’s Still Needed in the 21st Century SARAH J. GREENWALD,ANNE M. LEGGETT, AND JILL E. THOMLEY This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of ‘‘mathematical community’’ is Participants from the Special Session in Number Theory at the broadest: ‘‘schools’’ of mathematics, circles of AWM’s 40th Anniversary Celebration. Back row: Cristina Ballantine, Melanie Matchett Wood, Jackie Anderson, Alina correspondence, mathematical societies, student Bucur, Ekin Ozman, Adriana Salerno, Laura Hall-Seelig, Li-Mei organizations, extra-curricular educational activities Lim, Michelle Manes, Kristin Lauter; Middle row: Brooke Feigon, Jessica Libertini-Mikhaylov, Jen Balakrishnan, Renate (math camps, math museums, math clubs), and more. Scheidler; Front row: Lola Thompson, Hatice Sahinoglu, Bianca Viray, Alice Silverberg, Nadia Heninger. (Photo Cour- What we say about the communities is just as tesy of Kiran Kedlaya.) unrestricted. -
Buddhism and Responses to Disability, Mental Disorders and Deafness in Asia
Buddhism and Responses to Disability, Mental Disorders and Deafness in Asia. A bibliography of historical and modern texts with introduction and partial annotation, and some echoes in Western countries. [This annotated bibliography of 220 items suggests the range and major themes of how Buddhism and people influenced by Buddhism have responded to disability in Asia through two millennia, with cultural background. Titles of the materials may be skimmed through in an hour, or the titles and annotations read in a day. The works listed might take half a year to find and read.] M. Miles (compiler and annotator) West Midlands, UK. November 2013 Available at: http://www.independentliving.org/miles2014a and http://cirrie.buffalo.edu/bibliography/buddhism/index.php Some terms used in this bibliography Buddhist terms and people. Buddhism, Bouddhisme, Buddhismus, suffering, compassion, caring response, loving kindness, dharma, dukkha, evil, heaven, hell, ignorance, impermanence, kamma, karma, karuna, metta, noble truths, eightfold path, rebirth, reincarnation, soul, spirit, spirituality, transcendent, self, attachment, clinging, delusion, grasping, buddha, bodhisatta, nirvana; bhikkhu, bhikksu, bhikkhuni, samgha, sangha, monastery, refuge, sutra, sutta, bonze, friar, biwa hoshi, priest, monk, nun, alms, begging; healing, therapy, mindfulness, meditation, Gautama, Gotama, Maitreya, Shakyamuni, Siddhartha, Tathagata, Amida, Amita, Amitabha, Atisha, Avalokiteshvara, Guanyin, Kannon, Kuan-yin, Kukai, Samantabhadra, Santideva, Asoka, Bhaddiya, Khujjuttara, -
Proquest Dissertations
Daoxuan's vision of Jetavana: Imagining a utopian monastery in early Tang Item Type text; Dissertation-Reproduction (electronic) Authors Tan, Ai-Choo Zhi-Hui Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 25/09/2021 09:09:41 Link to Item http://hdl.handle.net/10150/280212 INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are In typewriter face, while others may be from any type of connputer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overiaps. ProQuest Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 DAOXUAN'S VISION OF JETAVANA: IMAGINING A UTOPIAN MONASTERY IN EARLY TANG by Zhihui Tan Copyright © Zhihui Tan 2002 A Dissertation Submitted to the Faculty of the DEPARTMENT OF EAST ASIAN STUDIES In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2002 UMI Number: 3073263 Copyright 2002 by Tan, Zhihui Ai-Choo All rights reserved. -
A Bounded Jump for the Bounded Turing Degrees
A bounded jump for the bounded Turing degrees Bernard A. Anderson Barbara F. Csima ∗ Department of Pure Mathematics Department of Pure Mathematics University of Waterloo University of Waterloo [email protected] [email protected] www.math.uwaterloo.ca/∼b7anders www.math.uwaterloo.ca/∼csima Abstract b We define the bounded jump of A by A = fx 2 ! j 9i ≤ x['i(x) # A'i(x) nb ^ Φx (x)#]g and let A denote the n-th bounded jump. We demon- strate several properties of the bounded jump, including that it is strictly increasing and order preserving on the bounded Turing (bT ) degrees (also known as the weak truth-table degrees). We show that the bounded jump is related to the Ershov hierarchy. Indeed, for n ≥ 2 we have nb n nb X ≤bT ; () X is ! -c.e. () X ≤1 ; , extending the classical 0 result that X ≤bT ; () X is !-c.e.. Finally, we prove that the ana- logue of Shoenfield inversion holds for the bounded jump on the bounded b 2b Turing degrees. That is, for every X such that ; ≤bT X ≤bT ; , there b b is a Y ≤bT ; such that Y ≡bT X. 1 Introduction In computability theory, we are interested in comparing the relative computa- tional complexities of infinite sets of natural numbers. There are many ways of doing this, and which method is used often depends on the purpose of the study, or how fine a comparison is desired. Two sets of the same computational com- plexity (X ≤ Y and Y ≤ X) are said to be in the same degree. -
President's Report
Newsletter VOLUME 43, NO. 6 • NOVEMBER–DECEMBER 2013 PRESIDENT’S REPORT As usual, summer flew by all too quickly. Fall term is now in full swing, and AWM is buzzing with activity. Advisory Board. The big news this fall is the initiation of an AWM Advisory Board. The Advisory Board, first envisioned under Georgia Benkart’s presidency, con- The purpose of the Association for Women in Mathematics is sists of a diverse group of individuals in mathematics and related disciplines with distinguished careers in academia, industry, or government. Through their insights, • to encourage women and girls to breadth of experience, and connections with broad segments of the mathematical study and to have active careers in the mathematical sciences, and community, the Board will seek to increase the effectiveness of AWM, help with fund- • to promote equal opportunity and raising, and contribute to a forward-looking vision for the organization. the equal treatment of women and Members of the Board were selected to represent a broad spectrum of academia girls in the mathematical sciences. and industry. Some have a long history with AWM, and others are new to the orga- nization; all are committed to forwarding our goals. We are pleased to welcome the following Board members: Mary Gray, Chair (American University) Jennifer Chayes (Microsoft Research) Nancy Koppel (Boston University) Irwin Kra (Stony Brook University) Joan Leitzel (University of New Hampshire, Ohio State University) Jill Mesirov (Broad Institute) Linda Ness (Applied Communication Sciences) Richard Schaar (Texas Instruments) IN THIS ISSUE Mary Spilker (Pfizer) Jessica Staddon (Google) 4 AWM Election 14 Benkart Named In addition, the President, Past President (or President Elect) and Executive Noether Lecturer Director of AWM are also members of the Board. -
President's Report
AWM ASSOCIATION FOR WOMEN IN MATHE MATICS Volume 36, Number l NEWSLETTER March-April 2006 President's Report Hidden Help TheAWM election results are in, and it is a pleasure to welcome Cathy Kessel, who became President-Elect on February 1, and Dawn Lott, Alice Silverberg, Abigail Thompson, and Betsy Yanik, the new Members-at-Large of the Executive Committee. Also elected for a second term as Clerk is Maura Mast.AWM is also pleased to announce that appointed members BettyeAnne Case (Meetings Coordi nator), Holly Gaff (Web Editor) andAnne Leggett (Newsletter Editor) have agreed to be re-appointed, while Fern Hunt and Helen Moore have accepted an extension of their terms as Member-at-Large, to join continuing members Krystyna Kuperberg andAnn Tr enk in completing the enlarged Executive Committee. I look IN THIS ISSUE forward to working with this wonderful group of people during the coming year. 5 AWM ar the San Antonio In SanAntonio in January 2006, theAssociation for Women in Mathematics Joint Mathematics Meetings was, as usual, very much in evidence at the Joint Mathematics Meetings: from 22 Girls Just Want to Have Sums the outstanding mathematical presentations by women senior and junior, in the Noerher Lecture and the Workshop; through the Special Session on Learning Theory 24 Education Column thatAWM co-sponsored withAMS and MAA in conjunction with the Noether Lecture; to the two panel discussions thatAWM sponsored/co-sponsored.AWM 26 Book Review also ran two social events that were open to the whole community: a reception following the Gibbs lecture, with refreshments and music that was just right for 28 In Memoriam a networking event, and a lunch for Noether lecturer Ingrid Daubechies. -
THERE IS NO DEGREE INVARIANT HALF-JUMP a Striking
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 125, Number 10, October 1997, Pages 3033{3037 S 0002-9939(97)03915-4 THERE IS NO DEGREE INVARIANT HALF-JUMP RODNEY G. DOWNEY AND RICHARD A. SHORE (Communicated by Andreas R. Blass) Abstract. We prove that there is no degree invariant solution to Post's prob- lem that always gives an intermediate degree. In fact, assuming definable de- terminacy, if W is any definable operator on degrees such that a <W (a) < a0 on a cone then W is low2 or high2 on a cone of degrees, i.e., there is a degree c such that W (a)00 = a for every a c or W (a)00 = a for every a c. 00 ≥ 000 ≥ A striking phenomenon in the early days of computability theory was that every decision problem for axiomatizable theories turned out to be either decidable or of the same Turing degree as the halting problem (00,thecomplete computably enumerable set). Perhaps the most influential problem in computability theory over the past fifty years has been Post’s problem [10] of finding an exception to this rule, i.e. a noncomputable incomplete computably enumerable degree. The problem has been solved many times in various settings and disguises but the so- lutions always involve specific constructions of strange sets, usually by the priority method that was first developed (Friedberg [2] and Muchnik [9]) to solve this prob- lem. No natural decision problems or sets of any kind have been found that are neither computable nor complete. The question then becomes how to define what characterizes the natural computably enumerable degrees and show that none of them can supply a solution to Post’s problem. -
On Relations Between Adams Spectral Sequences, with an Application to the Stable Homotopy of a Moore Space
Journal of Pure and Applied Algebra 20 (1981) 287-312 0 North-Holland Publishing Company ON RELATIONS BETWEEN ADAMS SPECTRAL SEQUENCES, WITH AN APPLICATION TO THE STABLE HOMOTOPY OF A MOORE SPACE Haynes R. MILLER* Harvard University, Cambridge, MA 02130, UsA Communicated by J.F. Adams Received 24 May 1978 0. Introduction A ring-spectrum B determines an Adams spectral sequence Ez(X; B) = n,(X) abutting to the stable homotopy of X. It has long been recognized that a map A +B of ring-spectra gives rise to information about the differentials in this spectral sequence. The main purpose of this paper is to prove a systematic theorem in this direction, and give some applications. To fix ideas, let p be a prime number, and take B to be the modp Eilenberg- MacLane spectrum H and A to be the Brown-Peterson spectrum BP at p. For p odd, and X torsion-free (or for example X a Moore-space V= So Up e’), the classical Adams E2-term E2(X;H) may be trigraded; and as such it is E2 of a spectral sequence (which we call the May spectral sequence) converging to the Adams- Novikov Ez-term E2(X; BP). One may say that the classical Adams spectral sequence has been broken in half, with all the “BP-primary” differentials evaluated first. There is in fact a precise relationship between the May spectral sequence and the H-Adams spectral sequence. In a certain sense, the May differentials are the Adams differentials modulo higher BP-filtration. One may say the same for p=2, but in a more attenuated sense. -
Periodic Phenomena in the Classical Adams Spectral
TRANSACTIONS of the AMERICAN MATHEMATICAL SOCIETY Volume 300. Number 1. March 1987 PERIODIC PHENOMENAIN THE CLASSICAL ADAMSSPECTRAL SEQUENCE MARK MAH0WALD AND PAUL SHICK Abstract. We investigate certain periodic phenomena in the classical Adams sepctral sequence which are related to the polynomial generators v„ in ot„(BP). We define the notion of a class a in Ext^ (Z/2, Z/2) being t>„-periodic or t>„-torsion and prove that classes that are u„-torsion are also uA.-torsion for all k such that 0 < k < «. This allows us to define a chromatic filtration of ExtA (Z/2, Z/2) paralleling the chromatic filtration of the Novikov spectral sequence £rterm given in [13]. 1. Introduction and statement of results. This work is motivated by a desire to understand something of the periodic phenomena noticed by Miller, Ravenel and Wilson in their work on the Novikov spectral sequence from the point of view of the classical Adams spectral sequence. The iij-term of the classical Adams spectral sequence (hereafter abbreviated clASS) is isomorphic to Ext A(Z/2, Z/2), where A is the mod 2 Steenrod algebra. This has been calculated completely in the range t — s < 70 [17]. The stem-by-stem calculation is quite tedious, though, so one looks for more global sorts of phenomena. The first result in this direction was the discovery of a periodic family in 7r*(S°) and their representatives in Ext A(Z/2, Z/2), discussed by Adams in [2] and by Barratt in [4]. This stable family, which is present for all primes p, is often denoted by {a,} and is thought of as v1-periodic, where y, is the polynomial generator of degree 2( p - 1) in 77+(BP)= Z^Jdj, v2,.. -
An Introduction to Computability Theory
AN INTRODUCTION TO COMPUTABILITY THEORY CINDY CHUNG Abstract. This paper will give an introduction to the fundamentals of com- putability theory. Based on Robert Soare's textbook, The Art of Turing Computability: Theory and Applications, we examine concepts including the Halting problem, properties of Turing jumps and degrees, and Post's Theo- rem.1 In the paper, we will assume the reader has a conceptual understanding of computer programs. Contents 1. Basic Computability 1 2. The Halting Problem 2 3. Post's Theorem: Jumps and Quantifiers 3 3.1. Arithmetical Hierarchy 3 3.2. Degrees and Jumps 4 3.3. The Zero-Jump, 00 5 3.4. Post's Theorem 5 Acknowledgments 8 References 8 1. Basic Computability Definition 1.1. An algorithm is a procedure capable of being carried out by a computer program. It accepts various forms of numerical inputs including numbers and finite strings of numbers. Computability theory is a branch of mathematical logic that focuses on algo- rithms, formally known in this area as computable functions, and studies the degree, or level of computability that can be attributed to various sets (these concepts will be formally defined and elaborated upon below). This field was founded in the 1930s by many mathematicians including the logicians: Alan Turing, Stephen Kleene, Alonzo Church, and Emil Post. Turing first pioneered computability theory when he introduced the fundamental concept of the a-machine which is now known as the Turing machine (this concept will be intuitively defined below) in his 1936 pa- per, On computable numbers, with an application to the Entscheidungsproblem[7]. -
The Adams-Novikov Spectral Sequence and the Homotopy Groups of Spheres
The Adams-Novikov Spectral Sequence and the Homotopy Groups of Spheres Paul Goerss∗ Abstract These are notes for a five lecture series intended to uncover large-scale phenomena in the homotopy groups of spheres using the Adams-Novikov Spectral Sequence. The lectures were given in Strasbourg, May 7–11, 2007. May 21, 2007 Contents 1 The Adams spectral sequence 2 2 Classical calculations 5 3 The Adams-Novikov Spectral Sequence 10 4 Complex oriented homology theories 13 5 The height filtration 21 6 The chromatic decomposition 25 7 Change of rings 29 8 The Morava stabilizer group 33 ∗The author were partially supported by the National Science Foundation (USA). 1 9 Deeper periodic phenomena 37 A note on sources: I have put some references at the end of these notes, but they are nowhere near exhaustive. They do not, for example, capture the role of Jack Morava in developing this vision for stable homotopy theory. Nor somehow, have I been able to find a good way to record the overarching influence of Mike Hopkins on this area since the 1980s. And, although, I’ve mentioned his name a number of times in this text, I also seem to have short-changed Mark Mahowald – who, more than anyone else, has a real and organic feel for the homotopy groups of spheres. I also haven’t been very systematic about where to find certain topics. If I seem a bit short on references, you can be sure I learned it from the absolutely essential reference book by Doug Ravenel [27] – “The Green Book”, which is not green in its current edition. -
Stable Homotopy and the Adams Spectral Sequence
FACULTY OF SCIENCE UNIVERSITY OF COPENHAGEN Master Project in Mathematics Paolo Masulli Stable homotopy and the Adams Spectral Sequence Advisor: Jesper Grodal Handed-in: January 24, 2011 / Revised: March 20, 2011 CONTENTS i Abstract In the first part of the project, we define stable homotopy and construct the category of CW-spectra, which is the appropriate setting for studying it. CW-spectra are particular spectra with properties that resemble CW-complexes. We define the homotopy groups of CW- spectra, which are connected to stable homotopy groups of spaces, and we define homology and cohomology for CW-spectra. Then we construct the Adams spectral sequence, in the setting of the category of CW-spectra. This spectral sequence can be used to get information about the stable homotopy groups of spaces. The last part of the project is devoted to calculations. We show two examples of the use of the Adams sequence, the first one applied to the stable homotopy groups of spheres and the second one to the homotopy of the spectrum ko of the connective real K-theory. Contents Introduction 1 1 Stable homotopy 2 1.1 Generalities . .2 1.2 Stable homotopy groups . .2 2 Spectra 3 2.1 Definition and homotopy groups . .3 2.2 CW-Spectra . .4 2.3 Exact sequences for a cofibration of CW-spectra . 11 2.4 Cohomology for CW-spectra . 13 3 The Adams Spectral Sequence 17 3.1 Exact resolutions . 17 3.2 Constructing the spectral sequence . 18 3.3 The main theorem . 20 4 Calculations 25 4.1 Stable homotopy groups of spheres .