Part of Institute of Mathematical Statistics Monographs
Publication planned for: April 2015
availability: Not yet published - available from June 2015
This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Frechet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of transformations - in particular, similarity, reflection similarity, affine and projective transformations. In addition, nonparametric Bayesian theory is adapted and extended to manifolds for the purposes of density estimation, regression and classification. Ideal for statisticians who analyze manifold data and wish to develop their own methodology, this book is also of interest to probabilists, mathematicians, computer scientists, and morphometricians with mathematical training.
1. Introduction
2. Examples
3. Location and spread on metric spaces
4. Extrinsic analysis on manifolds
5. Intrinsic analysis on manifolds
6. Landmark-based shape spaces
7. Kendall's similarity shape spaces ƒ°km
8. The planar shape space ƒ°k2
9. Reflection similarity shape spaces Rƒ°km
10. Stiefel manifolds
11. Affine shape spaces Aƒ°km
12. Real projective spaces and projective shape spaces
13. Nonparametric Bayes inference
14. Regression, classification and testing
i. Differentiable manifolds
ii. Riemannian manifolds
iii. Dirichlet processes
iv. Parametric models on Sd and ƒ°k2
References
Subject index.
Part of London Mathematical Society Student Texts
Publication planned for: July 2015
availability: Not yet published - available from July 2015
format: Hardback
isbn: 9781107107991
format: Paperback
isbn: 9781107518438
The projective and polar geometries that arise from a vector space over a finite field are particularly useful in the construction of combinatorial objects, such as latin squares, designs, codes and graphs. This book provides an introduction to these geometries and their many applications to other areas of combinatorics. Coverage includes a detailed treatment of the forbidden subgraph problem from a geometrical point of view, and a chapter on maximum distance separable codes, which includes a proof that such codes over prime fields are short. The author also provides more than 100 exercises (complete with detailed solutions), which show the diversity of applications of finite fields and their geometries. Finite Geometry and Combinatorial Applications is ideal for anyone, from a third-year undergraduate to a researcher, who wishes to familiarise themselves with and gain an appreciation of finite geometry.
1. Fields
2. Vector spaces
3. Forms
4. Geometries
5. Combinatorial applications
6. The forbidden subgraph problem
7. MDS codes
References
Index.
Part of London Mathematical Society Lecture Note Series
Publication planned for: July 2015
availability: Not yet published - available from July 2015
format: Paperback
isbn: 9781107462540
The 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern overview of the subject for graduate students in arithmetic geometry and Diophantine geometry. It is also essential reading for any researcher wishing to keep abreast of the latest developments in the field. Highlights include Tim Browning's survey on applications of the circle method to rational points on algebraic varieties and Per Salberger's chapter on rational points on cubic hypersurfaces.
Preface Luis Dieulefait, D. R. Heath-Brown, Gerd Faltings, Yuri I. Manin, B. Z. Moroz and Jean-Pierre Wintenberger
Introduction
List of participants
Trimester seminar
Workshop on the Serre conjecture
The research conference
1. Galois groups of local fields, Lie algebras, and ramification Victor Abrashkin
2. A characterisation of ordinary modular eigenforms with CM Rajender Adibhatla and Panagiotis Tsaknias
3. Selmer complexes and p-adic Hodge theory Denis Benois
4. A survey of applications of the circle method to rational points T. D. Browning
5. Arithmetic differential equations of Painleve VI type Alexandru Buium and Yuri I. Manin
6. Differential calculus with integers Alexandru Buium
7. Un calcul de groupe de Brauer et une application arithmetique Jean-Louis Colliot-Thelene
8. Connectedness of Hecke algebras and the Rayuela conjecture: a path to functoriality and modularity Luis Dieulefait and Ariel Pacetti
9. Big image of Galois representations and congruence ideals Haruzo Hida and Jacques Tilouine
10. The skew-symmetric pairing on the Lubin?Tate formal module M. A. Ivanov and S. V. Vostokov
11. Equations in matrix groups and algebras over number fields and rings: prolegomena to a lowbrow noncommutative Diophantine geometry Boris Kunyavski?
12. On the ?-adic regulator as an ingredient of Iwasawa theory L. V. Kuz'min
13. On a counting problem for G-shtukas Ngo Dac Tuan
14. Modular forms and Calabi?Yau varieties Kapil Paranjape and Dinakar Ramakrishnan
15. Derivative of symmetric square p-adic L-functions via pull-back formula Giovanni Rosso
16. Uniform bounds for rational points on cubic hypersurfaces Per Salberger
17. Descent on toric fibrations Alexei N. Skorobogatov
18. On filtrations of vector bundles over P1Z A. Smirnov
19. On the dihedral Euler characteristics of Selmer groups of Abelian varieties Jeanine van Order
20. CM values of higher Green's functions and regularized Petersson products Maryna Viazovska.
Part of Encyclopedia of Mathematics and its Applications
Publication planned for: September 2015
availability: Not yet published - available from September 2015
format: Hardback
isbn: 9781107109636
In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Grobner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugere (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Part VII. Beyond:
46. Zacharias
47. Bergman
48. Ufnarovski
49. Weispfenning
50. Spear2
51. Weispfenning II
52. Sweedler
53. Hironaka
54. Hironaka II
55. Janet
56. Macaulay V
57. Gerdt and Faugere
Bibliography
Index.