Point Counting And The Zilber Pink Conjecture
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Point Counting And The Zilber Pink Conjecture
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Author : Jonathan Pila
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
Point Counting And The Zilber Pink Conjecture written by Jonathan Pila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Mathematics categories.
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.
Point Counting And The Zilber Pink Conjecture
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Author : Jonathan Pila
language : en
Publisher:
Release Date : 2022
Point Counting And The Zilber Pink Conjecture written by Jonathan Pila and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with MATHEMATICS categories.
Point Counting And The Zilber Pink Conjecture
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Author : Jonathan Pila
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
Point Counting And The Zilber Pink Conjecture written by Jonathan Pila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Mathematics categories.
Explores the recent spectacular applications of point-counting in o-minimal structures to functional transcendence and diophantine geometry.
Variations On A Theme Of Borel
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Author : Shmuel Weinberger
language : en
Publisher: Cambridge University Press
Release Date : 2022-12-08
Variations On A Theme Of Borel written by Shmuel Weinberger and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-08 with Mathematics categories.
Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.
Large Deviations For Markov Chains
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Author : Alejandro D. de Acosta
language : en
Publisher:
Release Date : 2022-10-12
Large Deviations For Markov Chains written by Alejandro D. de Acosta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-12 with Mathematics categories.
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.
Fractional Sobolev Spaces And Inequalities
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Author : D. E. Edmunds
language : en
Publisher: Cambridge University Press
Release Date : 2022-10-13
Fractional Sobolev Spaces And Inequalities written by D. E. Edmunds and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-13 with Mathematics categories.
Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.
Families Of Varieties Of General Type
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Author : János Kollár
language : en
Publisher: Cambridge University Press
Release Date : 2023-04-20
Families Of Varieties Of General Type written by János Kollár and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-20 with Mathematics categories.
The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.
O Minimality And Diophantine Geometry
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Author : G. O. Jones
language : en
Publisher: Cambridge University Press
Release Date : 2015-08-13
O Minimality And Diophantine Geometry written by G. O. Jones and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-13 with Mathematics categories.
This book brings the researcher up to date with recent applications of mathematical logic to number theory.
Annales Scientifiques De L Cole Normale Sup Rieure
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Author : École normale supérieure (France)
language : en
Publisher:
Release Date : 2016
Annales Scientifiques De L Cole Normale Sup Rieure written by École normale supérieure (France) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Electronic journals categories.
Some Problems Of Unlikely Intersections In Arithmetic And Geometry
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Author : Umberto Zannier
language : en
Publisher: Princeton University Press
Release Date : 2012-03-25
Some Problems Of Unlikely Intersections In Arithmetic And Geometry written by Umberto Zannier and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-25 with Mathematics categories.
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).