Part of Cambridge Tracts in Mathematics
Product details
Publication planned for: August 2015
format: Hardback
isbn: 9781107124394
dimensions: 228 x 152 mm
contains: 4 b/w illus.
Ridge functions are a rich class of simple multivariate functions which have found applications in a variety of areas. These include partial differential equations (where they are sometimes termed 'plane waves'), computerised tomography, projection pursuit in the analysis of large multivariate data sets, the MLP model in neural networks, Waring's problem over linear forms, and approximation theory. Ridge Functions is the first book devoted to studying them as entities in and of themselves. The author describes their central properties and provides a solid theoretical foundation for researchers working in areas such as approximation or data science. He also includes an extensive bibliography and discusses some of the unresolved questions that may set the course for future research in the field.
Preface
Glossary of selected symbols
1. Introduction
2. Smoothness
3. Uniqueness
4. Identifying functions and directions
5. Polynomial ridge functions
6. Density and representation
7. Closure
8. Existence and characterization of best approximations
9. Approximation algorithms
10. Integral representations
11. Interpolation at points
12. Interpolation on lines
References
Supplemental references
Author index
Subject index.
Part of London Mathematical Society Lecture Note Series
Product details
Publication planned for: December 2015
format: Paperback
isbn: 9781107514546
dimensions: 228 x 152 mm
contains: 15 b/w illus.
availability: Not yet published - available from December 2015
Every four years, leading researchers gather to survey the latest developments in all aspects of group theory. Since 1981, the proceedings of those meetings have provided a regular snapshot of the state of the art in group theory and helped to shape the direction of research in the field. This volume contains selected papers from the 2013 meeting held in St Andrews. It begins with major articles from each of the four main speakers: Emmanuel Breuillard (Paris-Sud), Martin Liebeck (Imperial College London), Alan Reid (Texas) and Karen Vogtmann (Cornell). These are followed by, in alphabetical order, survey articles contributed by other conference participants, which cover a wide spectrum of modern group theory.
Introduction C. M. Campbell and E. F. Robertson
1. Approximate subgroups and super-strong approximation Emmanuel Breuillard
2. Width questions for finite simple groups Martin W. Liebeck
3. Profinite properties of discrete groups Alan W. Reid
4. GL(n,Z), Out(Fn) and everything in between: automorphism groups of RAAGs Karen Vogtmann
5. Permutation groups and transformation semigroups: results and problems Joao Araujo and Peter J. Cameron
6. New progress on factorized groups and subgroup permutability Milagros Arroyo-Jorda, Paz Arroyo-Jorda, Ana Martinez-Pastor and M. Dolores Perez-Ramos
7. A survey on the normalizer problem for integral group rings Andreas Bachle
8. A survey on Clifford?Fischer Theory Ayoub B. M. Basheer and Jamshid Moori
9. A generalisation on the solvability of finite groups with three class sizes for normal subgroups Antonio Beltran and Maria Jose Felipe
10. Automorphism groups of non-orientable Riemann surfaces E. Bujalance, F. J. Cirre, J. J. Etayo, G. Gromadzki and E. Martinez
11. What are the C2-groups? Inna Capdeboscq and Christopher Parker
12. Resurrecting Wells' exact sequence and Buckley's group action Jill Dietz
13. Recent work on Beauville surfaces, structures and groups Ben Fairbairn
14. Something for nothing: some consequences of the solution of the Tarski problems Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger and Dennis Spellman
15. The groups of projectivities in finite planes Theo Grundhofer
16. On the relation gap and relation lifting problem Jens Harlander
17. Some results on products of finite subsets in groups Marcel Herzog, Patrizia Longobardi and Mercede Maj
18. Formal languages and group theory Sam A. M. Jones and Richard M. Thomas
19. On the Castelnuovo?Mumford regularity of the cohomology of fusion systems and of the Hochschild cohomology of block algebras Radha Kessar and Markus Linckelmann
20. Recent advances on torsion subgroups of integral group rings Wolfgang Kimmerle and Alexander Konovalov
21. On finite groups with small prime spectrum Anatoly S. Kondratiev and Igor V. Khramtsov
22. Solvability criteria for finite loops and groups Emma Leppala
23. The rational subset membership problem for groups: a survey Markus Lohrey
24. A survey of Milnor laws Olga Macedo?ska
25. Capable p-groups Arturo Magidin and Robert Fitzgerald Morse
26. On the normal structure of a finite group with restrictions on the maximal subgroups N. V. Maslova and D. O. Revin
27. Certain monomial characters and their normal constituents Gabriel Navarro and Carolina Vallejo
28. Recognition of finite quasi-simple groups by the degrees of their irreducible representations Hung Ngoc Nguyen and Hung P. Tong-Viet
29. Generalized Baumslag?Solitar groups: a survey of recent progress Derek J. S. Robinson
30. Zeta functions of groups and rings ? recent developments Christopher Voll.
Asterisque, Number: 369
215; 374 pp; softcover
ISBN-13: 978-2-85629-805-3
This volume contains the first part of the proceedings of the conference held at Paris-Sud University, Orsay, from June 25-June 29, 2012, to celebrate Gerard Laumon's 60th birthday. The range of subjects covered reflects the diversity and richness of the works and interests of Gerard Laumon: etale cohomology of schemes and stacks, l-adic sheaves and Fourier transform, character sheaves, classic and geometric Langlands correspondence, Grothendieck-Lefschetz trace formula, Arthur-Selberg trace formula, Shimura varieties, Higgs fibre bundles and Hitchin fibration.
Graduate students and research mathematicians.
Asterisque,Number: 370
2015; 304 pp; softcover
ISBN-13: 978-2-85629-806-0
This volume contains the second part of the proceedings of the conference held at Paris-Sud University, Orsay, from June 25- June 29, 2012, to celebrate Gerard Laumon's 60th birthday. The range of subjects covered reflects the diversity and richness of the works and interests of Gerard Laumon: etale cohomology of schemes and stacks, l-adic sheaves and Fourier transform, character sheaves, classic and geometric Langlands correspondence, Grothendieck-Lefschetz trace formula, Arthur-Selberg trace formula, Shimura varieties, Higgs fibre bundles and Hitchin fibration.
Graduate students and research mathematicians.
Asterisque,Number: 371
2015; 239 pp; softcover
ISBN-13: 978-2-85629-807-7
The authors describe a new approach to relative p-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of both Berkovich and Huber. They give a thorough development of Ó-modules over a relative Robba ring associated to a perfect Banach ring of characteristic p, including the relationship between these objects and etale Zp-local systems and Qp-local systems on the algebraic and analytic spaces associated to the base ring, and the relationship between (pro-)etale cohomology and Ó-cohomology. They also make a critical link to mixed characteristic by exhibiting an equivalence of tensor categories between the finite etale algebras over an arbitrary perfect Banach algebra over a nontrivially normed complete field of characteristic p and the finite etale algebras over a corresponding Banach Qp-algebra. This recovers the homeomorphism between the absolute Galois groups of Fp((Î)) and Qp(Ęp) given by the field of norms construction of Fontaine and Wintenberger, as well as generalizations considered by Andreatta, Brinon, Faltings, Gabber, Ramero, Scholl, and, most recently, Scholze.
Using Huber's formalism of adic spaces and Scholze's formalism of perfectoid spaces, the authors globalize the constructions to give several descriptions of the etale local systems on analytic spaces over p-adic fields. One of these descriptions uses a relative version of the Fargues-Fontaine curve.
Graduate students and research mathematicians.
Memoires de la Societe Mathematique de France, Number: 140/141
2015; 386 pp; softcover
ISBN-13: 978-2-85629-811-4
A note to readers: This book is in French.
In this work, the author extends the theory of motives, as developed by Voevodsky and Morel-Voevodsky, to the context of rigid analytic geometry over a complete nonarchimedean field.
The first chapter deals with the homotopical approach of Morel and Voevodsky. In this chapter the author discusses the construction of the motivic stable homotopy category of rigid analytic varieties and a complete description of this category in terms of algebraic motives when the base field has equal characteristic zero and its valuation is discrete.
The second chapter deals with Voevodsky's approach based on transfers. In this chapter the author discusses the construction of the triangulated category of rigid analytic motives, and an extension to rigid analytic geometry of a large number of Voevodsky's fundamental results such as his theory of homotopy invariants presheaves with transfers.
The present work is a lot more than just a mere copy of the classical theory and the reader will find a lot of results that are new and specific to rigid analytic geometry.
Graduate students and research mathematicians.