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Point Counting And The Zilber Pink Conjecture
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Book Synopsis Point-Counting and the Zilber–Pink Conjecture by : Jonathan Pila
Download or read book Point-Counting and the Zilber–Pink Conjecture written by Jonathan Pila and published by Cambridge University Press. This book was released on 2022-06-09 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores the recent spectacular applications of point-counting in o-minimal structures to functional transcendence and diophantine geometry.
Book Synopsis Point-Counting and the Zilber–Pink Conjecture by : Jonathan Pila
Download or read book Point-Counting and the Zilber–Pink Conjecture written by Jonathan Pila and published by Cambridge University Press. This book was released on 2022-06-09 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Families of Varieties of General Type by : János Kollár
Download or read book Families of Varieties of General Type written by János Kollár and published by Cambridge University Press. This book was released on 2023-04-30 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.
Book Synopsis Fractional Sobolev Spaces and Inequalities by : D. E. Edmunds
Download or read book Fractional Sobolev Spaces and Inequalities written by D. E. Edmunds and published by Cambridge University Press. This book was released on 2022-10-31 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.
Book Synopsis Variations on a Theme of Borel by : Shmuel Weinberger
Download or read book Variations on a Theme of Borel written by Shmuel Weinberger and published by Cambridge University Press. This book was released on 2022-11-30 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.
Book Synopsis Large Deviations for Markov Chains by : Alejandro D. de Acosta
Download or read book Large Deviations for Markov Chains written by Alejandro D. de Acosta and published by . This book was released on 2022-10-12 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis O-Minimality and Diophantine Geometry by : G. O. Jones
Download or read book O-Minimality and Diophantine Geometry written by G. O. Jones and published by Cambridge University Press. This book was released on 2015-08-20 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre–Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila–Wilkie theorem, bounds on Galois orbits, and functional transcendence results. All of these topics are covered in this volume, making it ideal for researchers wishing to keep up to date with the latest developments in the field. Original papers are combined with background articles in both the number theoretic and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura varieties, and Jacob Tsimerman's proof via o-minimality of Ax's theorem on the functional case of Schanuel's conjecture.
Book Synopsis Some Problems of Unlikely Intersections in Arithmetic and Geometry by : Umberto Zannier
Download or read book Some Problems of Unlikely Intersections in Arithmetic and Geometry written by Umberto Zannier and published by Princeton University Press. This book was released on 2012-03-25 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Book Synopsis Around the Zilber-Pink Conjecture by : Philipp Habegger
Download or read book Around the Zilber-Pink Conjecture written by Philipp Habegger and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Following Faltings and Vojta's work proving the Mordell-Lang conjecture for abelian varieties and Raynaud's work proving the Manin-Mumford conjecture, many new diophantine questions appeared, often described as problems of unlikely intersections. The arithmetic of moduli spaces of abelian varieties and, more generally, Shimura varieties has been parallel-developed around the central André-Oort conjecture. These two themes can be placed in a common frame--the Zilber-Pink conjecture. This volume is an introduction to these problems and to the various techniques used: geometry, height theory, reductive groups and Hodge theory, Shimura varieties, and model theory via the notion of o-minimal structure."--Publisher.
Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Boyan Sirakov
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Boyan Sirakov and published by World Scientific. This book was released on 2019-02-27 with total page 5393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Book Synopsis Annales Scientifiques de L'École Normale Supérieure by : École normale supérieure (France)
Download or read book Annales Scientifiques de L'École Normale Supérieure written by École normale supérieure (France) and published by . This book was released on 2016 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Heights in Diophantine Geometry by : Enrico Bombieri
Download or read book Heights in Diophantine Geometry written by Enrico Bombieri and published by Cambridge University Press. This book was released on 2006 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.
Book Synopsis Cambridge Tracts in Mathematics by : Jean Bertoin
Download or read book Cambridge Tracts in Mathematics written by Jean Bertoin and published by Cambridge University Press. This book was released on 1996 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.
Book Synopsis Skin in the Game by : Nassim Nicholas Taleb
Download or read book Skin in the Game written by Nassim Nicholas Taleb and published by Random House. This book was released on 2018-02-27 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: #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.”
Download or read book Fewnomials written by A. G. Khovanskiĭ and published by American Mathematical Soc.. This book was released on 1991 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis O-Minimality and Diophantine Geometry by : G. O. Jones
Download or read book O-Minimality and Diophantine Geometry written by G. O. Jones and published by Cambridge University Press. This book was released on 2015-08-13 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings the researcher up to date with recent applications of mathematical logic to number theory.
Book Synopsis Mathematical Logic by : Roman Kossak
Download or read book Mathematical Logic written by Roman Kossak and published by Springer. This book was released on 2018-10-03 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
