'Life of Pi' by Yann Martel Reading and Responding
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An Introduction to the Trace Formula
Clay Mathematics Proceedings Volume 4, 2005 An Introduction to the Trace Formula James Arthur Contents Foreword 3 Part I. The Unrefined Trace Formula 7 1. The Selberg trace formula for compact quotient 7 2. Algebraic groups and adeles 11 3. Simple examples 15 4. Noncompact quotient and parabolic subgroups 20 5. Roots and weights 24 6. Statement and discussion of a theorem 29 7. Eisenstein series 31 8. On the proof of the theorem 37 9. Qualitative behaviour of J T (f) 46 10. The coarse geometric expansion 53 11. Weighted orbital integrals 56 12. Cuspidal automorphic data 64 13. A truncation operator 68 14. The coarse spectral expansion 74 15. Weighted characters 81 Part II. Refinements and Applications 89 16. The first problem of refinement 89 17. (G, M)-families 93 18. Localbehaviourofweightedorbitalintegrals 102 19. The fine geometric expansion 109 20. Application of a Paley-Wiener theorem 116 21. The fine spectral expansion 126 22. The problem of invariance 139 23. The invariant trace formula 145 24. AclosedformulaforthetracesofHeckeoperators 157 25. Inner forms of GL(n) 166 Supported in part by NSERC Discovery Grant A3483. c 2005 Clay Mathematics Institute 1 2 JAMES ARTHUR 26. Functoriality and base change for GL(n) 180 27. The problem of stability 192 28. Localspectraltransferandnormalization 204 29. The stable trace formula 216 30. Representationsofclassicalgroups 234 Afterword: beyond endoscopy 251 References 258 Foreword These notes are an attempt to provide an entry into a subject that has not been very accessible. The problems of exposition are twofold. It is important to present motivation and background for the kind of problems that the trace formula is designed to solve. -
Challenging Humanism: Human-Animal Relations in Recent Postcolonial Novels
Middlesex University Research Repository An open access repository of Middlesex University research http://eprints.mdx.ac.uk Borrell, Sally (2009) Challenging humanism: human-animal relations in recent postcolonial novels. PhD thesis, Middlesex University. [Thesis] Final accepted version (with author’s formatting) This version is available at: https://eprints.mdx.ac.uk/6520/ Copyright: Middlesex University Research Repository makes the University’s research available electronically. Copyright and moral rights to this work are retained by the author and/or other copyright owners unless otherwise stated. The work is supplied on the understanding that any use for commercial gain is strictly forbidden. A copy may be downloaded for personal, non-commercial, research or study without prior permission and without charge. Works, including theses and research projects, may not be reproduced in any format or medium, or extensive quotations taken from them, or their content changed in any way, without first obtaining permission in writing from the copyright holder(s). They may not be sold or exploited commercially in any format or medium without the prior written permission of the copyright holder(s). Full bibliographic details must be given when referring to, or quoting from full items including the author’s name, the title of the work, publication details where relevant (place, publisher, date), pag- ination, and for theses or dissertations the awarding institution, the degree type awarded, and the date of the award. If you believe that any material held in the repository infringes copyright law, please contact the Repository Team at Middlesex University via the following email address: [email protected] The item will be removed from the repository while any claim is being investigated. -
Chapter 2 C -Algebras
Chapter 2 C∗-algebras This chapter is mainly based on the first chapters of the book [Mur90]. Material bor- rowed from other references will be specified. 2.1 Banach algebras Definition 2.1.1. A Banach algebra C is a complex vector space endowed with an associative multiplication and with a norm k · k which satisfy for any A; B; C 2 C and α 2 C (i) (αA)B = α(AB) = A(αB), (ii) A(B + C) = AB + AC and (A + B)C = AC + BC, (iii) kABk ≤ kAkkBk (submultiplicativity) (iv) C is complete with the norm k · k. One says that C is abelian or commutative if AB = BA for all A; B 2 C . One also says that C is unital if 1 2 C , i.e. if there exists an element 1 2 C with k1k = 1 such that 1B = B = B1 for all B 2 C . A subalgebra J of C is a vector subspace which is stable for the multiplication. If J is norm closed, it is a Banach algebra in itself. Examples 2.1.2. (i) C, Mn(C), B(H), K (H) are Banach algebras, where Mn(C) denotes the set of n × n-matrices over C. All except K (H) are unital, and K (H) is unital if H is finite dimensional. (ii) If Ω is a locally compact topological space, C0(Ω) and Cb(Ω) are abelian Banach algebras, where Cb(Ω) denotes the set of all bounded and continuous complex func- tions from Ω to C, and C0(Ω) denotes the subset of Cb(Ω) of functions f which vanish at infinity, i.e. -
Addition to Summer Letter
May 2020 Dear Student, You are enrolled in Advanced Placement English Literature and Composition for the coming school year. Bowling Green High School has offered this course since 1983. I thought that I would tell you a little bit about the course and what will be expected of you. Please share this letter with your parents or guardians. A.P. Literature and Composition is a year-long class that is taught on a college freshman level. This means that we will read college level texts—often from college anthologies—and we will deal with other materials generally taught in college. You should be advised that some of these texts are sophisticated and contain mature themes and/or advanced levels of difficulty. In this class we will concentrate on refining reading, writing, and critical analysis skills, as well as personal reactions to literature. A.P. Literature is not a survey course or a history of literature course so instead of studying English and world literature chronologically, we will be studying a mix of classic and contemporary pieces of fiction from all eras and from diverse cultures. This gives us an opportunity to develop more than a superficial understanding of literary works and their ideas. Writing is at the heart of this A.P. course, so you will write often in journals, in both personal and researched essays, and in creative responses. You will need to revise your writing. I have found that even good students—like you—need to refine, mature, and improve their writing skills. You will have to work diligently at revising major essays. -
LIFE of PI a Fox 2000 Pictures Presentation
MOVIE REVIEW Afr J Psychiatry 2013;16:219 LIFE OF PI A Fox 2000 Pictures Presentation. A Haishang Films / Gil Netter Production. A Film by Ang Lee Film reviewed by Franco P. Visser From the multi award-winning director With the animals destined for and film maker Ang Lee ( Crouching overseas clients, the Patel family Tiger Hidden Dragon, Brokeback boards a Japanese cargo vessel Mountain, Sense and Sensibility ) bound for Canada where the Patel comes a magical and epic film about family hopes to make a new life for the tragic and extraordinary life of Pi themselves following the loss of the Patel. Pi was given the names ‘Piscine zoo. A heavy storm ensues one night Molitor’ by his respected uncle whom whilst travelling to Canada and the he referred to as Mamaji, a famous ship sinks. Pi and the Bengal tiger Indian swimmer, who named him Richard Parker becomes castaways after the famed art deco swimming at sea with no hope of being pool complex next to the Bois de rescued. A magical and adventurous Boulogne Park in Paris. The Piscine journey starts for both Pi and the Molitor swimming pool was built in tiger, and both need to learn to live the late 1920’s and opened by together on a small lifeboat in the amongst others the famous Johnny middle of the Pacific Ocean. As Weissmuller. This pool was also mentioned earlier, a hyena, a zebra where Louis Réard introduced and and an orang-utan also survived the popularised the bikini. Now sadly sinking ship, although needless to closed and vandalised by graffiti say that confined along with a Bengal artists and the like, the Piscine Molitor tiger on a small wooden lifeboat, the remains a landmark historical former three animals do not survive. -
Notes on the Chern-Character Maakestad H* Department of Mathematics, NTNU, Trondheim, Norway
Theory an ie d L A p d p Maakestad, J Generalized Lie Theory Appl 2017, 11:1 e l z i i c l a a t Journal of Generalized Lie r DOI: 10.4172/1736-4337.1000253 i o e n n s e G ISSN: 1736-4337 Theory and Applications Research Article Open Access Notes on the Chern-Character Maakestad H* Department of Mathematics, NTNU, Trondheim, Norway Abstract Notes for some talks given at the seminar on characteristic classes at NTNU in autumn 2006. In the note a proof of the existence of a Chern-character from complex K-theory to any cohomology Lie theory with values in graded Q-algebras equipped with a theory of characteristic classes is given. It respects the Adams and Steenrod operations. Keywords: Chern-character; Chern-classes; Euler classes; Singular H* : Top→−Q algebras cohomology; De Rham-cohomology; Complex K-theory; Adams operations; Steenrod operations from the category of topological spaces to the category of graded commutative Q-algebras with respect to continuous maps of topological Introduction spaces. We say the theory satisfy the projective bundle property if the The aim of this note is to give an axiomatic and elementary following axioms are satisfied: For any rankn complex continuous treatment of Chern-characters of vectorbundles with values in a vectorbundle E over a compact space B There is an Euler class. class of cohomology-theories arising in topology and algebra. Given ∈ 2 uE H (P(E)) (1) a theory of Chern-classes for complex vectorbundles with values in → singular cohomology one gets in a natural way a Chern-character from Where π:P(E) B is the projective bundle associated to E. -
GROUP REPRESENTATIONS and CHARACTER THEORY Contents 1
GROUP REPRESENTATIONS AND CHARACTER THEORY DAVID KANG Abstract. In this paper, we provide an introduction to the representation theory of finite groups. We begin by defining representations, G-linear maps, and other essential concepts before moving quickly towards initial results on irreducibility and Schur's Lemma. We then consider characters, class func- tions, and show that the character of a representation uniquely determines it up to isomorphism. Orthogonality relations are introduced shortly afterwards. Finally, we construct the character tables for a few familiar groups. Contents 1. Introduction 1 2. Preliminaries 1 3. Group Representations 2 4. Maschke's Theorem and Complete Reducibility 4 5. Schur's Lemma and Decomposition 5 6. Character Theory 7 7. Character Tables for S4 and Z3 12 Acknowledgments 13 References 14 1. Introduction The primary motivation for the study of group representations is to simplify the study of groups. Representation theory offers a powerful approach to the study of groups because it reduces many group theoretic problems to basic linear algebra calculations. To this end, we assume that the reader is already quite familiar with linear algebra and has had some exposure to group theory. With this said, we begin with a preliminary section on group theory. 2. Preliminaries Definition 2.1. A group is a set G with a binary operation satisfying (1) 8 g; h; i 2 G; (gh)i = g(hi)(associativity) (2) 9 1 2 G such that 1g = g1 = g; 8g 2 G (identity) (3) 8 g 2 G; 9 g−1 such that gg−1 = g−1g = 1 (inverses) Definition 2.2. -
Reading Yann Martel's Life of Pi
INTERNATIONAL JOURNAL FOR INNOVATIVE RESEARCH IN MULTIDISCIPLINARY FIELD ISSN: 2455-0620 Volume - 6, Issue - 8, Aug – 2020 Monthly, Peer-Reviewed, Refereed, Indexed Journal with IC Value: 86.87 Impact Factor: 6.719 Received Date: 01/08/2020 Acceptance Date: 18/08/2020 Publication Date: 31/08/2020 A Saga of Human Resilience: Reading Yann Martel’s Life of Pi Ankita Pandey Research Scholar, Department of English and MEL University of Lucknow, Lucknow, Uttar Pradesh, India Email - [email protected] Abstract: Resilience is all about shifting our perceptions, changing our responses, and experiencing real growth. It is well defined by an American author Elizabeth Edwards “Resilience is accepting your new reality, even if it's less good than the one you had before. You can fight it, you can do nothing but scream about what you've lost, or you can accept that and try to put together something that's good”(“Resilience Remembered”, 2010). Resilient people often have a good sense of humour, patience, action-oriented approach, faith, optimism, tolerance of negative effect, adaptability to change etc. Whether an individual or a group of people, we have numerous examples of people who proved themselves and started their lives again after being badly affected by hazardous situations. Literature has promiscuous stories that deal with human resilience and one of them is Yann Martel’s masterpiece Life of Pi that was published in 2001. Life of Pi is a story of an Indian Tamil boy named Piscine Molitor Patel who was later nicknamed as “Pi”. The story of the novel revolves around the life of Pi who faced a shipwreck and had to survive on a lifeboat in the Pacific Ocean with a Bengal Tiger for 227 days. -
L-Functions and Non-Abelian Class Field Theory, from Artin to Langlands
L-functions and non-abelian class field theory, from Artin to Langlands James W. Cogdell∗ Introduction Emil Artin spent the first 15 years of his career in Hamburg. Andr´eWeil charac- terized this period of Artin's career as a \love affair with the zeta function" [77]. Claude Chevalley, in his obituary of Artin [14], pointed out that Artin's use of zeta functions was to discover exact algebraic facts as opposed to estimates or approxi- mate evaluations. In particular, it seems clear to me that during this period Artin was quite interested in using the Artin L-functions as a tool for finding a non- abelian class field theory, expressed as the desire to extend results from relative abelian extensions to general extensions of number fields. Artin introduced his L-functions attached to characters of the Galois group in 1923 in hopes of developing a non-abelian class field theory. Instead, through them he was led to formulate and prove the Artin Reciprocity Law - the crowning achievement of abelian class field theory. But Artin never lost interest in pursuing a non-abelian class field theory. At the Princeton University Bicentennial Conference on the Problems of Mathematics held in 1946 \Artin stated that `My own belief is that we know it already, though no one will believe me { that whatever can be said about non-Abelian class field theory follows from what we know now, since it depends on the behavior of the broad field over the intermediate fields { and there are sufficiently many Abelian cases.' The critical thing is learning how to pass from a prime in an intermediate field to a prime in a large field. -
Geometry of Character Varieties of Surface Groups
GEOMETRY OF CHARACTER VARIETIES OF SURFACE GROUPS MOTOHICO MULASE∗ Abstract. This article is based on a talk delivered at the RIMS{OCAMI Joint International Conference on Geometry Related to Integrable Systems in September, 2007. Its aim is to review a recent progress in the Hitchin integrable systems and character varieties of the fundamental groups of Riemann surfaces. A survey on geometric aspects of these character varieties is also provided as we develop the exposition from a simple case to more elaborate cases. Contents 1. Introduction 1 2. Character varieties of finite groups and representation theory 2 3. Character varieties of Un as moduli spaces of stable vector bundles 5 4. Twisted character varieties of Un 6 5. Twisted character varieties of GLn(C) 10 6. Hitchin integrable systems 13 7. Symplectic quotient of the Hitchin system and mirror symmetry 16 References 21 1. Introduction The character varieties we consider in this article are the set of equivalence classes Hom(π1(Σg);G)=G of representations of a surface group π1(Σg) into another group G. Here Σg is a closed oriented surface of genus g, which is assumed to be g ≥ 2 most of the time. The action of G on the space of homomorphisms is through the conjugation action. Since this action has fixed points, the quotient requires a special treatment to make it a reasonable space. Despite the simple appearance of the space, it has an essential connection to many other subjects in mathematics ([1, 2, 6, 9, 10, 11, 14, 15, 17, 19, 24, 25, 33, 34]), and the list is steadily growing ([4, 7, 12, 13, 18, 23]). -
Stpps High School English – Parent Guidance
STPPS HIGH SCHOOL ENGLISH – PARENT GUIDANCE ABOUT LOUISIANA’S ELA GUIDEBOOKS ELA Guidebooks is an English language arts curriculum for core instruction. Made by teachers for teachers, the Guidebook units ensure all students can read, understand, and express their understanding of complex, grade-level texts, ensuring their readiness for college or a career. In the ELA Guidebooks, students: ● explore central questions that connect units in a yearlong pathway; ● examine texts by multiple authors about substantive topics; ● engage in varied opportunities to read, discuss, write, and present; and ● experience integrated instruction and assessment leading to a comprehensive ELA experience. THE STPPS HIGH SCHOOL ENGLISH EXPERIENCE The highly acclaimed texts we explore through our high school English curriculum provide opportunities for students to analyze traditional literature and modern classics in order to examine significant questions. At the high school level, texts of appropriate complexity for college and career readiness inevitably cover topics that are more sophisticated. As one of the aims of education is to help students be ready for life beyond high school, it is essential for students to engage with texts representing authentic issues within society. Additionally, it is important for students to receive an age-appropriate educational experience. Every text is vetted by teachers, district staff, and community members and all high school English teachers receive training and resources connected to the implementation of curriculum. Teachers are prepared with the tools they need to ensure students are both engaged in complex thinking and experiencing age-appropriate content. Finally, we would like to provide all parents and guardians the opportunity to ask questions about our high school English curriculum, teacher training, or instructional process. -
Life of Pi, Historiography, and Psychotherapy
Frausel/1 Rebecca Frausel B.A., English Literature and Psychology Honors Thesis, Spring 2010 Life of Pi, Historiography, and Psychotherapy Thesis Defense: March 31, 2010 Revised: April 3, 2010 Committee Members: Primary Advisor: Karen Jacobs, Associate Professor, Honors Council Representative, Department of English Janice Ho, Assistant Professor, Department of English Secondary Advisor: Mary Klages, Associate Professor, Department of English Mithi Mukherjee, Assistant Professor, Department of History Frausel/2 And better had they ne’er been born, Who read to doubt, or read to scorn. --Sir Walter Scott Maybe God’s silence is an appeal to get beyond factuality. Maybe God’s trick is to call us through the imagination. If you don’t have any imagination, you live a diminished life. The overly reasonable life is a shrunken life. So much alienation in Western cultures is due to an excess of reason. --Yann Martel Frausel/3 Table of Contents Abstract…………………………………………………………………...…………...4 1. Introduction…………………………………………………………………...…….5 2. Hayden White’s “The Historical Text as Literary Artifact”……….………...……..8 3. Narrative Structure: Unspinning the Yarn of Life of Pi….………………..………15 4. Motif #1: Politics………………………………………………………..………...28 5. Motif #2: Anthropomorphism and Zoomorphism…..…………………..…….......32 6. Parallel Stories…...……………………………………………………..…………39 6.1. The Story With Animals and the Story Without Animals………..…………41 6.2. The Narrator and Martel………..…………………………………………...54 7. Conclusion……….……….……………………………………………….………56 Endnotes….…………………..………………………………………………………59 Works Cited.…………………..………………………………………………..……61 Frausel/4 Abstract This thesis explores the relationship between historiography and psychotherapy through an analysis of Yann Martel’s 2001 novel Life of Pi using Hayden White’s essay “The Historical Text as Literary Artifact.” The use of historiography as a psychotherapeutic technique is a fairly recurrent theme in our culture.