Series: Lecture Notes in Mathematics, Vol. 2109
2014, Approx. 120 p. 10 illus.
Softcover
ISBN 978-3-319-06476-5
Due: August 6, 2014
Only reference for the secondary height function for reducible buildings
Self-contained introduction to the study of finiteness properties of arithmetic groups
Many illustrations
Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.
Content Level ≫ Research
Keywords ≫ 20G30,22E40,20E42,51E24,57M07,20F65 - Arithmetic groups - CAT(0) geometry - Combinatorial Morse theory - Finiteness properties of groups - Twin-buildings
Related subjects ≫ Algebra - Geometry & Topology
Basic Definitions and Properties.- Finiteness Properties of G(Fq[t]).- Finiteness Properties of G(Fq[t; t1]).- Affine Kac-Moody Groups.- Adding Places.
Series: Lecture Notes in Mathematics, Vol. 2110
2014, Approx. 130 p.
Softcover
ISBN 978-3-319-06372-0
Due: August 5, 2014
Providing an up-to-date overview of the geometry of manifolds with non-negative sectional curvature, this volume gives a detailed account of the most recent research in the area. The lectures cover a wide range of topics such as general isometric group actions, circle actions on positively curved four manifolds, cohomogeneity one actions on Alexandrov spaces, isometric torus actions on Riemannian manifolds of maximal symmetry rank, n-Sasakian manifolds, isoparametric hypersurfaces in spheres, contact CR and CR submanifolds, Riemannian submersions and the Hopf conjecture with symmetry. Also included is an introduction to the theory of exterior differential systems.
Content Level ≫ Research
Keywords ≫ 53C21;57S25;53C23;58A15;58A20.22Exx;22Fxx,53Cxx; - Cohomogeneity one action - Lie group action - Non-negative sectional curvature - Riemannian manifolds - n-Sasakian manifolds
Related subjects ≫ Analysis - Geometry & Topology
Riemannian manifolds with positive sectional curvature.- An introduction to isometric group actions.- A note on maximal symmetry rank, quasipositive curvature and low dimensional manifolds.- Lectures on n-Sasakian manifolds.- On the Hopf conjecture with symmetry.- An Introduction to Exterior Differential Systems.
Series: Publications of the Scuola Normale Superiore, Vol. 13
Subseries: Lecture Notes (Scuola Normale Superiore)
2014, Approx. 275 p.
Softcover
ISBN 978-88-7642-497-7
Due: October 3, 2014
Based on several years teaching experience
Revised edition of two previous publications
Includes several applications
This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown out of a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several years of teaching experience in the subject. The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Ito's formula. The second part deals with differential stochastic equations and their connection with parabolic problems. The third part provides an introduction to the Malliavin calculus. Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems. In this third edition several small improvements are added and a new section devoted to the differentiability of the Feynman-Kac semigroup is introduced. A considerable number of corrections and improvements have been made.
Content Level ≫ Graduate
Keywords ≫ Brownian motion - Feynman-Kac semigroup - Gaussian measure - Malliavin calculus
Related subjects ≫ Scuola Normale Superiore
Introduction.- 1 Gaussian measures in Hilbert spaces.- 2 Gaussian random variables.- 3 The Malliavin derivative.- 4 Brownian Motion.- 5 Markov property of Brownian motion.- 6 Ito’s integral.- 7 Ito’s formula.- 8 Stochastic differential equations.- 9 Relationship between stochastic and parabolic equations.- 10 Formulae of Feynman?Kac and Girsanov.- 11 Malliavin calculus.- 12 Asymptotic behaviour of transition semigroups.- A The Dynkin Theorem.- B Conditional expectation.- C Martingales.- D Fixed points depending on parameters.- E A basic ergodic theorem.- References.
Series: Advanced Courses in Mathematics - CRM Barcelona, Vol. 27
2014, Approx. 170 p.
Softcover
ISBN 978-3-0348-0839-2
Due: August 31, 2014
Features a concise introduction to variable Lebesgue spaces requiring only basic knowledge of analysis
Includes an easy-to-read introduction to the classical problems as well as to recent developments in the asymptotic theory for hyperbolic equations
The presentation of the material starts at a basic level but gives several deeper insights into different aspects of the theories up to the most recent developments
This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts.
Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted.
Part 2 gives an overview of the asymptotic properties of solutions to hyperbolic equations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems with time-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Cauchy problems are constructed as oscillatory integrals by working in appropriate time-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lower order terms can change asymptotic properties and thus complements the exposition.
Content Level ≫ Research
Keywords ≫ Rubio de Francia extrapolation - hyperbolic Cauchy problems - maximal operators - oscillating time-dependent coefficients - singular integrals - variable Lebesgue spaces
Related subjects ≫ Birkhauser Mathematics
Part I: Introduction to the Variable Lebesgue Spaces.- Introduction and motivation.- Properties of variable Lebesgue spaces.- The Hardy-Littlewood maximal operator.- Extrapolation in variable Lebesgue spaces.- Part II: Asymptotic Behaviour of Solutions to Hyperbolic Equations and Systems.- Equations with constant coefficients.- Some interesting model cases.- Time-dependent hyperbolic systems.- Effective lower order perturbations.- Examples and counter-examples.- Related topics
Series: Lecture Notes in Mathematics, Vol. 2111
Subseries: C.I.M.E. Foundation Subseries
2014, XII, 250 p.
Softcover
ISBN 978-3-642-54935-9
Due: August 21, 2014
Presentation of a seminar result (Wilkie's o-minimality of the real exponential field) through a series of exercises
Extended expository article on the model theory of valued fields, an area with many current researchers and a lack of good expositions
Wide-ranging and up-to-date overview of undecidability and Hilbert's Tenth Problem, linking model theory, number theory, and algebraic geometry
Exposition of recent breakthrough in abstract model theory, around NIP theories
Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
Content Level ≫ Research
Keywords ≫ Decidable theory - Dependent theory - Exponential field - Model theory - Valued field
Related subjects ≫ Algebra - Analysis - Mathematics - Number Theory and Discrete Mathematics