Centenary of the borel conjecture, 

Автор: John Coates; Peter Schneider; R. Sujatha; Otmar Ve
Название: Noncommutative Iwasawa Main Conjectures over Totally Real Fields
ISBN: 3642443354 ISBN-13(EAN): 9783642443350
Издательство: Springer
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Описание: The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.

Автор: Shmuel Weinberger
Название: Variations on a Theme of Borel: An Essay on the Role of the Fundamental Group in Rigidity
ISBN: 1107142598 ISBN-13(EAN): 9781107142596
Издательство: Cambridge Academ
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Описание: Shmuel Weinberger describes here analogies between geometric topology, differential geometry, group theory, global analysis, and noncommutative geometry. He develops deep tools in a setting where they have immediate application. The connections between these fields enrich each and shed light on one another.

Автор: Murakami
Название: Volume Conjecture for Knots
ISBN: 9811311498 ISBN-13(EAN): 9789811311499
Издательство: Springer
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Описание: The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement.

Автор: Moriwaki, Atsushi (kyoto University, Japan) Ikoma, Hideaki Kawaguchi, Shu (doshisha University, Kyoto)
Название: Mordell conjecture
ISBN: 1108845959 ISBN-13(EAN): 9781108845953
Издательство: Cambridge Academ
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Описание: This book provides a self-contained proof of the Mordell conjecture (Faltings`s theorem) - one of the most important achievements in Diophantine geometry - alongside a concise introduction to the field of Diophantine geometry itself, at a level suitable for advanced undergraduate students and graduate students.

Название: The Willmore Conjecture & The Willm
ISBN: 149874463X ISBN-13(EAN): 9781498744638
Издательство: Taylor&Francis
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Описание: This book is the first monograph dedicated wholly to Willmore energy and surfaces as contemporary topics in differential geometry. It also sits at the intersection between integrable systems, harmonic maps, Lie groups, calculus of variations, geometric analysis and applied differential geometry.

Автор: Jason P. Bell, Dragos Ghioca, Thomas J. Tucker
Название: The Dynamical Mordell-Lang Conjecture
ISBN: 1470424088 ISBN-13(EAN): 9781470424084
Издательство: Mare Nostrum (Eurospan)
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Описание: The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point $x$ under the action of an endomorphism $f$ of a quasiprojective complex variety $X$. More precisely, it claims that for any point $x$ in $X$ and any subvariety $V$ of $X$, the set of indices $n$ such that the $n$-th iterate of $x$ under $f$ lies in $V$ is a finite union of arithmetic progressions. In this book the authors present all known results about the Dynamical Mordell-Lang Conjecture, focusing mainly on a $p$-adic approach which provides a parametrization of the orbit of a point under an endomorphism of a variety.

Автор: Wilfred W. J. Hulsbergen
Название: Conjectures in Arithmetic Algebraic Geometry
ISBN: 3528064331 ISBN-13(EAN): 9783528064334
Издательство: Springer
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Описание: In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro- duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich- let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper- ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza- tion of Dirichlet's L-functions with a generalization of class field the- ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory.

Автор: Alonso-gutierrez, David Bastero, Jesus
Название: Approaching the kannan-lovasz-simonovits and variance conjectures
ISBN: 3319132628 ISBN-13(EAN): 9783319132624
Издательство: Springer
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Описание: Focusing on two central conjectures of Asymptotic Geometric Analysis, the Kannan-Lovasz-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.

Автор: Armand Borel
Название: Introduction to Arithmetic Groups
ISBN: 1470452316 ISBN-13(EAN): 9781470452315
Издательство: Mare Nostrum (Eurospan)
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Описание: Fifty years after it was first published, Armand Borel`s Introduction aux groupes arithmetiques continues to be very important for the theory of arithmetic groups. In particular, Chapter III of the book remains the standard reference for fundamental results on reduction theory.

Автор: Armand Borel
Название: Oeuvres - Collected Papers IV
ISBN: 3642307175 ISBN-13(EAN): 9783642307171
Издательство: Springer
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Описание: Contains the papers published by A Borel from 1983 to 1999. This volume concludes with an essay on H Poincare and special relativity. Some comments on, and corrections to, a number of papers have been added.