The Weil Conjectures

The Weil Conjectures

Author: Karen Olsson

Publisher: Macmillan + ORM

Published: 2019-07-16

Total Pages: 167

ISBN-13: 0374719632

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A New York Times Editors' Pick and Paris Review Staff Pick "A wonderful book." --Patti Smith "I was riveted. Olsson is evocative on curiosity as an appetite of the mind, on the pleasure of glutting oneself on knowledge." --Parul Sehgal, The New York Times An eloquent blend of memoir and biography exploring the Weil siblings, math, and creative inspiration Karen Olsson’s stirring and unusual third book, The Weil Conjectures, tells the story of the brilliant Weil siblings—Simone, a philosopher, mystic, and social activist, and André, an influential mathematician—while also recalling the years Olsson spent studying math. As she delves into the lives of these two singular French thinkers, she grapples with their intellectual obsessions and rekindles one of her own. For Olsson, as a math major in college and a writer now, it’s the odd detours that lead to discovery, to moments of insight. Thus The Weil Conjectures—an elegant blend of biography and memoir and a meditation on the creative life. Personal, revealing, and approachable, The Weil Conjectures eloquently explores math as it relates to intellectual history, and shows how sometimes the most inexplicable pursuits turn out to be the most rewarding.


Conjectures and Refutations

Conjectures and Refutations

Author: Karl Raimund Popper

Publisher: Psychology Press

Published: 2002

Total Pages: 614

ISBN-13: 9780415285940

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Conjectures and Refutations is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.


Dangerous Conjectures

Dangerous Conjectures

Author: Brian Finney

Publisher: Kdp

Published: 2021-03-25

Total Pages: 280

ISBN-13: 9780999800331

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In Dangerous Conjectures, computer scientist Adam investigates QAnon, allied to a White House subverting the 2020 election. Covid-19 and a violent ex-boyfriend threaten his wife Julia.


Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform

Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform

Author: Reinhardt Kiehl

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 382

ISBN-13: 3662045761

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The authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories.


Conjectures in Arithmetic Algebraic Geometry

Conjectures in Arithmetic Algebraic Geometry

Author: Wilfred W. J. Hulsbergen

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 247

ISBN-13: 3663095053

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In the early 1980's, stimulated by work of Bloch and Deligne, Beilinson stated some intriguing conjectures on special values of L-functions of algebraic varieties defined over number fields. Roughly speaking these special values are determinants of higher regulator maps relating the higher algebraic K-groups of the variety to its cohomology. In this respect, higher algebraic K-theory is believed to provide a universal, motivic cohomology theory and the regulator maps are determined by Chern characters from higher algebraic K-theory to any other suitable cohomology theory. Also, Beilinson stated a generalized Hodge conjecture. This book provides an introduction to and a survey of Beilinson's conjectures and an introduction to Jannsen's work with respect to the Hodge and Tate conjectures. It addresses mathematicians with some knowledge of algebraic number theory, elliptic curves and algebraic K-theory.


Conjecture and Proof

Conjecture and Proof

Author: Miklos Laczkovich

Publisher: American Mathematical Soc.

Published: 2001-12-31

Total Pages: 118

ISBN-13: 1470458322

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The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on Conjecture and Proof. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of $e$, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.


Novikov Conjectures, Index Theorems, and Rigidity: Volume 1

Novikov Conjectures, Index Theorems, and Rigidity: Volume 1

Author: Steven C. Ferry

Publisher: Cambridge University Press

Published: 1995-11-23

Total Pages: 386

ISBN-13: 0521497965

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These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'.


Approaching the Kannan-Lovász-Simonovits and Variance Conjectures

Approaching the Kannan-Lovász-Simonovits and Variance Conjectures

Author: David Alonso-Gutiérrez

Publisher: Springer

Published: 2015-01-07

Total Pages: 159

ISBN-13: 3319132636

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Focusing on two central conjectures of Asymptotic Geometric Analysis, the Kannan-Lovász-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the treated topics. Offering a presentation suitable for professionals with little background in analysis, geometry or probability, the work goes directly to the connection between isoperimetric-type inequalities and functional inequalities, giving the interested reader rapid access to the core of these conjectures. In addition, four recent and important results in this theory are presented in a compelling way. The first two are theorems due to Eldan-Klartag and Ball-Nguyen, relating the variance and the KLS conjectures, respectively, to the hyperplane conjecture. Next, the main ideas needed prove the best known estimate for the thin-shell width given by Guédon-Milman and an approach to Eldan's work on the connection between the thin-shell width and the KLS conjecture are detailed.


Stark's Conjectures: Recent Work and New Directions

Stark's Conjectures: Recent Work and New Directions

Author: David Burns

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 234

ISBN-13: 0821834800

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Stark's conjectures on the behavior of USDLUSD-functions were formulated in the 1970s. Since then, these conjectures and their generalizations have been actively investigated. This has led to significant progress in algebraic number theory. The current volume, based on the conference held at Johns Hopkins University (Baltimore, MD), represents the state-of-the-art research in this area. The first four survey papers provide an introduction to a majority of the recent work related to themes currently under exploration in the area, such as non-abelian and USDpUSD-adic aspects of the conjectures, abelian refinements, etc. Among others, some important contributors to the volume include Harold M. Stark, John Tate, and interested in number theory.


Graph Theory

Graph Theory

Author: Ralucca Gera

Publisher: Springer

Published: 2016-10-19

Total Pages: 300

ISBN-13: 331931940X

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This is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-established mathematician will find the overall exposition engaging and enlightening. Each chapter, presented in a story-telling style, includes more than a simple collection of results on a particular topic. Each contribution conveys the history, evolution, and techniques used to solve the authors’ favorite conjectures and open problems, enhancing the reader’s overall comprehension and enthusiasm. The editors were inspired to create these volumes by the popular and well attended special sessions, entitled “My Favorite Graph Theory Conjectures," which were held at the winter AMS/MAA Joint Meeting in Boston (January, 2012), the SIAM Conference on Discrete Mathematics in Halifax (June,2012) and the winter AMS/MAA Joint meeting in Baltimore(January, 2014). In an effort to aid in the creation and dissemination of open problems, which is crucial to the growth and development of a field, the editors requested the speakers, as well as notable experts in graph theory, to contribute to these volumes.