ISBN: 978-2-85629-282-2
Series: Asterisque, Number 331
Published: 15 May 2010; Copyright Year: 2010; Pages: 469; Softcover
Graduate students and research mathematicians interested in number theory.
In this last volume on the local p -adic correspondence for GL2 (Qp ), the editors have gathered
papers which, mostly, do not use directly the (Ó, ¡ )-module theory. The methods and results are often
geometric (p -adic comparison theorems, de Rham cohomology of the Drinfeld half-plane), or global (localglobal
compatibility with etale completed cohomology). There are also papers on p -adic Hodge theory and
the L-invariant and important local results on extensions between certain representations of GL2 (Qp ).
G. Stevens -- Goleman's mathcal{L}-invariant and families of modular forms
P. Colmez -- Invariants mathcal{L} et derivees de valeurs propres de Frobenius
M. Bertolini, H. Darmon, and A. Iovita -- Families of automorphic forms on definite quaternion algebras and Teitelbaum's conjecture
C. Breuil -- Serie speciale p-adique et cohomologie etale completee
C. Breuil and A. Mezard -- Representations semi-stables de mathrm{GL}_2(mathbb{Q}_p), demi-plan p-adique et reduction modulo p
R. Coleman and A. Iovita -- Hidden structures on semistable curves
C. Breuil and M. Emerton -- Representations p-adiques ordinaires de mathbf{GL}_2(mathbf{Q}_p) et compatibilite local-global
V. Paknas -- Extensions for supersingular representations of mathrm{GL}_2(mathbb{Q}_p)
M. Emerton -- Ordinary parts of admissible representations of p-adic reductive groups I. Definition and first properties
M. Emerton -- Ordinary parts of admissible representations of p-adic reductive groups II. Derived functors
M. Emerton and V. Paknas -- On the effaceability of certain delta-functors
ISBN: 978-3-03719-086-9
Series: EMS Tracts in Mathematics, Volume 10
Published: 15 May 2010; Copyright Year: 2010; Pages: 290; Hardcove
Graduate students and research mathematicians interested in topological aspects of quantum field theory.
Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space.
This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on 2-dimensional and 3-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail.
The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Muger and A. Virelizier summarize their work in this area.
The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological
aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology.
Generalities on HQFTs
Group-algebras
Two-dimensional HQFTs
Biangular algebras and lattice HQFTs
Enumeration problems in dimension two
Crossed G-categories and invariants of links
Modular G-categories and HQFTs
Miscellaneous algebra
Appendix 1. Relative HQFTs
Appendix 2. State sum invariants of 3-dimensional G-manifolds
Appendix 3. Recent work on HQFTs
Appendix 4. Open problems
Appendix 5. On the structure of braided crossed G-categories
Appendix 6. Algebraic properties of Hopf G-coalgebras
Appendix 7. Invariants of 3-dimensional G-manifolds from Hopf coalgebras
Bibliography
Index
ISBN: 978-3-03719-085-2
Series: EMS Tracts in Mathematics, Volume 11
Published: 15 May 2010; Copyright Year: 2010; Pages: 305; Hardcover
Graduate students and research mathematicians interested in complexity theory and number theory.
The first chapters of this book deal with Haar bases, Faber bases and some spline bases for function
spaces in Euclidean n -space and n -cubes. These are used in the subsequent chapters to study sampling
and numerical integration preferably in spaces with dominating mixed smoothness. The subject of the last chapter is the symbiotic relationship between numerical integration and discrepancy, measuring the deviation of sets of points from uniformity.
This book is addressed to graduate students and mathematicians who have a working knowledge of basic elements of function spaces and approximation theory and who are interested in the subtle interplay between function spaces, complexity theory and number theory (discrepancy).
Function spaces
Haar bases
Faber bases
Sampling
Numerical integration
Discrepancy
Bibliography
List of Figures
Symbols
Index
ISBN: 978-3-03719-081-4
Series: EMS Textbooks in Mathematics, Volume 11
Published: 15 May 2010; Copyright Year: 2010; Pages: 363; Hardcover
Graduate students and research mathematicians interested in dynamical systems.
This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at ETH Zurich.
The first part centers around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearby. The orbit structure in such sets is analyzed by means of the shadowing lemma, whose proof is based on the contraction principle. This lemma is also used to prove S. Smalefs theorem
about the embedding of Bernoulli systems near homoclinic orbits. The chaotic behavior is illustrated in the simple mechanical model of a periodically perturbed mathematical pendulum.
The second part of the book is devoted to Hamiltonian systems. The Hamiltonian formalism is developed in the elegant language of the exterior calculus. The theorem of V. Arnold and R. Jost shows that the solutions
of Hamiltonian systems which possess sufficiently many integrals of motion can be written down explicitly and for all times. The existence proofs of global periodic orbits of Hamiltonian systems on symplecticmanifolds are based on a variational principle for the old action functional of classical mechanics. The necessary tools from variational calculus are developed.
There is an intimate relation between the periodic orbits of Hamiltonian systems and a class of symplectic invariants called symplectic capacities. From these symplectic invariants one derives surprising symplectic rigidity phenomena. This allows a first glimpse of the fast developing new field of symplectic topology.
ISBN: 978-2-85629-240-2
Series: Seminaires et Congres, Number 18
Published: 15 April 2010; Copyright Year: 2009; Pages: 466; Softcover
Graduate students and research mathematicians interested in negative or zero-curvature geometries, discrete groups and rigidities.
This volume gathers lecture notes taken at the 2004 Summer School, which was held at the Institut Fourier (Grenoble). The title of the Summer School (gNegative or zero-curvature geometries, discrete groups and rigiditiesh) has been used for the present volume. In many cases the lecture notes have been rewritten and enhanced.
1. Quelques groupes et geometries
J. Maubon -- Symmetric spaces of the non-compact type: Differential geometry
P.-E. Paradan -- Symmetric spaces of the non-compact type: Lie groups
G. Rousseau -- Euclidean buildings
Y. Benoist -- Five lectures on lattices in semisimple Lie groups
2. Quelques rigidites en geometrie differentielle
G. Besson -- Calabi-Weil infinitesimal rigidity
M. Bourdon -- Quasi-conformal geometry and Mostow rigidity
L. Bessieres -- Minimal volume
M. Burger and A. Iozzi -- A useful formula from bounded cohomology
3. Espaces metriques singuliers
G. Courtois -- Critical exponents and rigidity in negative curvature
C. Dru?u -- Quasi-isometry rigidity of groups
P. Pansu -- Superrigidite geometrique et applications harmoniques
4. Deformations, espaces de modules et compactifications
F. Paulin -- Sur la compactification de Thurston de l'espace de Teichmuller
A. Beauville -- Moduli of cubic surfaces and Hodge theory