Point Counting And The Zilber Pink Conjecture

Author : Jonathan Pila
Publisher : Cambridge University Press
Page : 268 pages
File Size : 53,7 Mb
Release : 2022-06-09
Category : Mathematics
ISBN : 9781009301923

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Point-Counting and the Zilber–Pink Conjecture by Jonathan Pila Pdf

Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.

Author : Jonathan Pila
Publisher : Unknown
Page : 128 pages
File Size : 41,5 Mb
Release : 2022
Category : MATHEMATICS
ISBN : 1009170317

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Point-counting and the Zilber-Pink Conjecture by Jonathan Pila Pdf

Author : János Kollár
Publisher : Cambridge University Press
Page : 491 pages
File Size : 40,7 Mb
Release : 2023-04-30
Category : Mathematics
ISBN : 9781009346108

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Families of Varieties of General Type by János Kollár Pdf

The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.

Author : D. E. Edmunds,W. D. Evans
Publisher : Cambridge University Press
Page : 169 pages
File Size : 47,8 Mb
Release : 2022-10-31
Category : Mathematics
ISBN : 9781009254632

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Fractional Sobolev Spaces and Inequalities by D. E. Edmunds,W. D. Evans Pdf

Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.

Author : Shmuel Weinberger
Publisher : Cambridge University Press
Page : 365 pages
File Size : 40,6 Mb
Release : 2022-11-30
Category : Mathematics
ISBN : 9781107142596

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Variations on a Theme of Borel by Shmuel Weinberger Pdf

Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.

Author : Alejandro D. de Acosta
Publisher : Unknown
Page : 264 pages
File Size : 54,7 Mb
Release : 2022-10-12
Category : Mathematics
ISBN : 9781009063357

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Large Deviations for Markov Chains by Alejandro D. de Acosta Pdf

This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.

Author : G. O. Jones,A. J. Wilkie
Publisher : Cambridge University Press
Page : 235 pages
File Size : 41,8 Mb
Release : 2015-08-13
Category : Mathematics
ISBN : 9781107462496

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O-Minimality and Diophantine Geometry by G. O. Jones,A. J. Wilkie Pdf

This book brings the researcher up to date with recent applications of mathematical logic to number theory.

Author : Umberto Zannier
Publisher : Princeton University Press
Page : 175 pages
File Size : 47,8 Mb
Release : 2012-03-25
Category : Mathematics
ISBN : 9781400842711

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Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181) by Umberto Zannier Pdf

This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension. The book is an expansion of the Hermann Weyl Lectures delivered by Umberto Zannier at the Institute for Advanced Study in Princeton in May 2010. The book consists of four chapters and seven brief appendixes, the last six by David Masser. The first chapter considers multiplicative algebraic groups, presenting proofs of several developments, ranging from the origins to recent results, and discussing many applications and relations with other contexts. The second chapter considers an analogue in arithmetic and several applications of this. The third chapter introduces a new method for approaching some of these questions, and presents a detailed application of this (by Masser and the author) to a relative case of the Manin-Mumford issue. The fourth chapter focuses on the André-Oort conjecture (outlining work by Pila).

Author : Jean Bertoin
Publisher : Cambridge University Press
Page : 292 pages
File Size : 55,8 Mb
Release : 1996
Category : Mathematics
ISBN : 0521646324

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Cambridge Tracts in Mathematics by Jean Bertoin Pdf

This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.

Author : CreateSpace Independent Publishing Platform,N a Krasil'nikov
Publisher : CreateSpace
Page : 346 pages
File Size : 55,7 Mb
Release : 2015-03-15
Category : Electronic
ISBN : 1508881901

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Soil Microorganisms and Higher Plants by CreateSpace Independent Publishing Platform,N a Krasil'nikov Pdf

This book is devoted to the problem of the interaction between soil microorganisms and higher plants. The material presented includes basic information on the structure, development, variability and classification of bacteria, actinomycetes and fungi in the light of recent scientific achievements, as well as information on the importance of microorganisms in plant nutrition, the role of micro-activities in the complementary nutrition of plants, the effect of microbes on the vitamin content of plants, their importance in plant development and their influence on soil fertility. In addition, data are given on the importance of antibiotics as a means of therapy and prevention of diseases in agricultural practice. The book is designed for the use of microbiologists. plant physiologists, soil specialists, phytopathologists, mycologists, agrobilologists, and agronomists. It may also serve as a textbook for students In biological faculties of universities or agricultural and forestry institutes.

Author : Nassim Nicholas Taleb
Publisher : Random House
Page : 305 pages
File Size : 53,9 Mb
Release : 2018-02-27
Category : Philosophy
ISBN : 9780425284636

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Skin in the Game by Nassim Nicholas Taleb Pdf

#1 NEW YORK TIMES BESTSELLER • A bold work from the author of The Black Swan that challenges many of our long-held beliefs about risk and reward, politics and religion, finance and personal responsibility In his most provocative and practical book yet, one of the foremost thinkers of our time redefines what it means to understand the world, succeed in a profession, contribute to a fair and just society, detect nonsense, and influence others. Citing examples ranging from Hammurabi to Seneca, Antaeus the Giant to Donald Trump, Nassim Nicholas Taleb shows how the willingness to accept one’s own risks is an essential attribute of heroes, saints, and flourishing people in all walks of life. As always both accessible and iconoclastic, Taleb challenges long-held beliefs about the values of those who spearhead military interventions, make financial investments, and propagate religious faiths. Among his insights: • For social justice, focus on symmetry and risk sharing. You cannot make profits and transfer the risks to others, as bankers and large corporations do. You cannot get rich without owning your own risk and paying for your own losses. Forcing skin in the game corrects this asymmetry better than thousands of laws and regulations. • Ethical rules aren’t universal. You’re part of a group larger than you, but it’s still smaller than humanity in general. • Minorities, not majorities, run the world. The world is not run by consensus but by stubborn minorities imposing their tastes and ethics on others. • You can be an intellectual yet still be an idiot. “Educated philistines” have been wrong on everything from Stalinism to Iraq to low-carb diets. • Beware of complicated solutions (that someone was paid to find). A simple barbell can build muscle better than expensive new machines. • True religion is commitment, not just faith. How much you believe in something is manifested only by what you’re willing to risk for it. The phrase “skin in the game” is one we have often heard but rarely stopped to truly dissect. It is the backbone of risk management, but it’s also an astonishingly rich worldview that, as Taleb shows in this book, applies to all aspects of our lives. As Taleb says, “The symmetry of skin in the game is a simple rule that’s necessary for fairness and justice, and the ultimate BS-buster,” and “Never trust anyone who doesn’t have skin in the game. Without it, fools and crooks will benefit, and their mistakes will never come back to haunt them.”

Author : Roman Kossak
Publisher : Springer
Page : 186 pages
File Size : 46,8 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9783319972985

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Mathematical Logic by Roman Kossak Pdf

This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.

Author : A. G. Khovanskiĭ
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 48,7 Mb
Release : 1991
Category : Mathematics
ISBN : 0821898302

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Fewnomials by A. G. Khovanskiĭ Pdf

The ideology of the theory of fewnomials is the following: real varieties defined by "simple", not cumbersome, systems of equations should have a "simple" topology. One of the results of the theory is a real transcendental analogue of the Bezout theorem: for a large class of systems of *k transcendental equations in *k real variables, the number of roots is finite and can be explicitly estimated from above via the "complexity" of the system. A more general result is the construction of a category of real transcendental manifolds that resemble algebraic varieties in their properties. These results give new information on level sets of elementary functions and even on algebraic equations. The topology of geometric objects given via algebraic equations (real-algebraic curves, surfaces, singularities, etc.) quickly becomes more complicated as the degree of the equations increases. It turns out that the complexity of the topology depends not on the degree of the equations but only on the number of monomials appearing in them. This book provides a number of theorems estimating the complexity of the topology of geometric objects via the cumbersomeness of the defining equations. In addition, the author presents a version of the theory of fewnomials based on the model of a dynamical system in the plane. Pfaff equations and Pfaff manifolds are also studied.

Author : James W. Cogdell,Günter Harder,Stephen Kudla,Freydoon Shahidi
Publisher : Springer
Page : 304 pages
File Size : 48,8 Mb
Release : 2018-08-18
Category : Mathematics
ISBN : 9783319955490

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Cohomology of Arithmetic Groups by James W. Cogdell,Günter Harder,Stephen Kudla,Freydoon Shahidi Pdf

This book discusses the mathematical interests of Joachim Schwermer, who throughout his career has focused on the cohomology of arithmetic groups, automorphic forms and the geometry of arithmetic manifolds. To mark his 66th birthday, the editors brought together mathematical experts to offer an overview of the current state of research in these and related areas. The result is this book, with contributions ranging from topology to arithmetic. It probes the relation between cohomology of arithmetic groups and automorphic forms and their L-functions, and spans the range from classical Bianchi groups to the theory of Shimura varieties. It is a valuable reference for both experts in the fields and for graduate students and postdocs wanting to discover where the current frontiers lie.

Author : Matthew C. H. Tointon
Publisher : Cambridge University Press
Page : 128 pages
File Size : 43,5 Mb
Release : 2019-11-14
Category : Mathematics
ISBN : 9781108571609

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Introduction to Approximate Groups by Matthew C. H. Tointon Pdf

Approximate groups have shot to prominence in recent years, driven both by rapid progress in the field itself and by a varied and expanding range of applications. This text collects, for the first time in book form, the main concepts and techniques into a single, self-contained introduction. The author presents a number of recent developments in the field, including an exposition of his recent result classifying nilpotent approximate groups. The book also features a considerable amount of previously unpublished material, as well as numerous exercises and motivating examples. It closes with a substantial chapter on applications, including an exposition of Breuillard, Green and Tao's celebrated approximate-group proof of Gromov's theorem on groups of polynomial growth. Written by an author who is at the forefront of both researching and teaching this topic, this text will be useful to advanced students and to researchers working in approximate groups and related areas.