Contemporary Mathematics, Volume: 542
2011; 284 pp; softcover
ISBN-13: 978-0-8218-4987-3
Expected publication date is May 29, 2011.
This volume contains the proceedings of a conference held in Cagliari, Italy, from September 7-10, 2009, to celebrate John C. Wood's 60th birthday.
These papers reflect the many facets of the theory of harmonic maps and its links and connections with other topics in Differential and Riemannian Geometry. Two long reports, one on constant mean curvature surfaces by F. Pedit and the other on the construction of harmonic maps by J. C. Wood, open the proceedings. These are followed by a mix of surveys on Prof. Wood's area of expertise: Lagrangian surfaces, biharmonic maps, locally conformally Kahler manifolds and the DDVV conjecture, as well as several research papers on harmonic maps. Other research papers in the volume are devoted to Willmore surfaces, Goldstein-Pedrich flows, contact pairs, prescribed Ricci curvature, conformal fibrations, the Fadeev-Hopf model, the Compact Support Principle and the curvature of surfaces.
Graduate students and research mathematicians interested in differential geometry and harmonic maps.
J. C. Wood -- Thirty-nine years of harmonic maps
A. Gerding, F. Pedit, and N. Schmitt -- Constant mean curvature surfaces: An integrable systems perspective
J. C. Wood -- Explicit constructions of harmonic maps
P. Baird and M. Wehbe -- Discrete harmonic map heat flow on a finite graph
G. Bande and D. Kotschick -- Contact pairs and locally conformally symplectic structures
E. Musso -- Congruence curves of the Goldstein-Petrich flows
H. Ma and Y. Ohnita -- Differential geometry of Lagrangian submanifolds and Hamiltonian variational problems
L. Ornea and M. Verbitsky -- A report on locally conformally Kahler manifolds
M. Rigoli, M. Salvatori, and M. Vignati -- k-Hessian differential inequalities and the compact support principle
H. Urakawa -- The geometry of biharmonic maps
G. Calvaruso -- Constructing metrics with prescribed geometry
J. Bolton and L. Fernandez -- On the regularity of the space of harmonic 2-spheres in the 4-sphere
S. Heller -- Conformal fibrations of mathbb{S}^3 by circles
K. Leschke -- Harmonic map methods for Willmore surfaces
F. Mercuri, S. Montaldo, and I. I. Onnis -- Some remarks on invariant surfaces and their extrinsic curvature
P. Baird, E. Loubeau, and C. Oniciuc -- Harmonic and biharmonic maps from surfaces
J. Jost and F. M. ?im?ir -- Non-divergence harmonic maps
R. Slobodeanu -- A note on higher-charge configurations for the Faddeev-Hopf model
J. Q. Ge and Z. Z. Tang -- A survey on the DDVV conjecture
G. Bande and A. Hadjar -- On the characteristic foliations of metric contact pairs
C.-L. Bejan -- A note on eta-Einstein manifolds
M. I. Munteanu and A. I. Nistor -- Minimal and flat surfaces in mathbb{H}^2timesmathbb{R} with canonical coordinates
R. C. Voicu -- Ricci curvature properties and stability on 3-dimensional Kenmotsu manifolds
S. Gudmundsson and M. Svensson -- On the existence of harmonic morphisms from three-dimensional Lie groups
Clay Mathematics Proceedings, Volume: 14
2011; 180 pp; softcover
ISBN-13: 978-0-8218-5205-7
Expected publication date is June 5, 2011.
This collection of cutting-edge articles on vector bundles and related topics originated from a CMI workshop, held in October 2006, that brought together a community indebted to the pioneering work of P. E. Newstead, visiting the United States for the first time since the 1960s. Moduli spaces of vector bundles were then in their infancy, but are now, as demonstrated by this volume, a powerful tool in symplectic geometry, number theory, mathematical physics, and algebraic geometry. In fact, the impetus for this volume was to offer a sample of the vital convergence of techniques and fundamental progress, taking place in moduli spaces at the outset of the twenty-first century.
This volume contains contributions by J. E. Andersen and N. L. Gammelgaard (Hitchin's projectively flat connection and Toeplitz operators), M. Aprodu and G. Farkas (moduli spaces), D. Arcara and A. Bertram (stability in higher dimension), L. Jeffrey (intersection cohomology), J. Kamnitzer (Langlands program), M. Lieblich (arithmetic aspects), P. E. Newstead (coherent systems), G. Pareschi and M. Popa (linear series on Abelian varieties), and M. Teixidor i Bigas (bundles over reducible curves).
These articles do require a working knowledge of algebraic geometry, symplectic geometry and functional analysis, but should appeal to practitioners in a diversity of fields. No specialization should be necessary to appreciate the contributions, or possibly to be stimulated to work in the various directions opened by these path-blazing ideas; to mention a few, the Langlands program, stability criteria for vector bundles over surfaces and threefolds, linear series over abelian varieties and Brauer groups in relation to arithmetic properties of moduli spaces.
Graduate students and research mathematics interested in algebraic, symplectic, and differential geometry.
J. E. Andersen and N. L. Gammelgaard -- Hitchin's projectively flat connection, Toeplitz operators and the asymptotic expasnion of TQFT curve operators
M. Aprodu and G. Farkas -- Koszul cohomology and applications to moduli
D. Arcara and A. Bertram -- Reider's theorem and Thaddeus pairs revisited
L. Jeffrey -- Intersection pairings in singular moduli spaces of bundles
J. Kamnitzer -- The Beilinson-Drinfeld Grassmannian and symplectic knot homology
M. Lieblich -- Arithmetic aspects of moduli spaces of sheaves on curves
P. E. Newstead -- Existence of alpha-stable coherent systems on algebraic curves
G. Pareschi and M. Popa -- Regularity on abelian varieties III: Relationship with generic vanishing and applications
M. Teixidor i Bigas -- Vector bundles on reducible curves and applications
Contemporary Mathematics, Volume: 543
2011; 277 pp; softcover
ISBN-13: 978-0-8218-4985-9
Expected publication date is June 25, 2011.
This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Representations of Reductive, p-adic Groups, which was held on January 16, 2010, in San Francisco, California.
One of the original guiding philosophies of harmonic analysis on p-adic groups was Harish-Chandra's Lefschetz principle, which suggested a strong analogy with real groups. From this beginning, the subject has developed a surprising variety of tools and applications. To mention just a few, Moy-Prasad's development of Bruhat-Tits theory relates analysis to group actions on locally finite polysimplicial complexes; the Aubert-Baum-Plymen conjecture relates the local Langlands conjecture to the Baum-Connes conjecture via a geometric description of the Bernstein spectrum; the p-adic analogues of classical symmetric spaces play an essential role in classifying representations; and character sheaves, originally developed by Lusztig in the context of finite groups of Lie type, also have connections to characters of p-adic groups.
The papers in this volume present both expository and research articles on these and related topics, presenting a broad picture of the current state of the art in p-adic harmonic analysis. The concepts are liberally illustrated with examples, usually appropriate for an upper-level graduate student in representation theory or number theory. The concrete case of the two-by-two special linear group is a constant touchstone.
Graduate students and research mathematicians interested in representations of p-adic groups.
P. N. Achar and C. L. R. Cunningham -- Toward a Mackey formula for compact restriction of character sheaves
J. D. Adler, S. DeBacker, P. J. Sally, Jr., and L. Spice -- Supercuspidal characters of SL_2 over a p-adic field
A.-M. Aubert, P. Baum, and R. Plymen -- Geometric structure in the representation theory of reductive p-adic groups II
B. Casselman -- The construction of Hecke algebras associated to a Coxeter group
J. Hakim and J. M Lansky -- Distinguished supercuspidal representations of SL_2
J.-L. Kim and J.-K. Yu -- Twisted Levi sequences and explicit types on Sp_4
F. Murnaghan -- Regularity and distinction of supercuspidal representations
M. Nevins -- Patterns in branching rules for irreducible representations of SL_2(k), for k a p-adic field
R. Portilla -- Parametrizing nilpotent orbits in p-adic symmetric spaces
S. Spallone -- An integration formula of Shahidi
M. H. Weissman -- Managing metaplectiphobia: Covering p-adic groups
Mathematical Surveys and Monographs, Volume: 173
2011; approx. 358 pp; hardcover
ISBN-13: 978-0-8218-4911-8
Expected publication date is July 13, 2011.
Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts.
This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
Graduate students and research mathematicians interested in the theory and practice of computational geometry.
The power of grids - closest pair and smallest enclosing disk
Quadtrees - hierarchical grids
Well-separated pair decomposition
Clustering - definitions and basic algorithms
On complexity, sampling, and varepsilon-nets and varepsilon-samples
Approximation via reweighting
Yet even more on sampling
Sampling and the moments technique
Depth estimation via sampling
Approximating the depth via sampling and emptiness
Random partition via shifting
Good triangulations and meshing
Approximating the Euclidean traveling salesman problem (TSP)
Approximating the Euclidean TSP using bridges
Linear programming in low dimensions
Polyhedrons, polytopes, and linear programming
Approximate nearest neighbor search in low dimension
Approximate nearest neighbor via point-location
The Johnson-Lindenstrauss lemma
Approximate nearest neighbor (ANN) search in high dimensions
Approximating a convex body by an ellipsoid
Approximating the minimum volume bounding box of a point set
Coresets
Approximation using shell sets
Duality
Finite metric spaces and partitions
Some probability and tail inequalities
Miscellaneous prerequisite
Bibliography
Index
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Student Mathematical Library, Volume: 59
2011; approx. 232 pp; softcover
ISBN-13: 978-0-8218-5351-1
Expected publication date is August 11, 2011.
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory.
The goal of this book is to give a "holistic" introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints.
The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Undergraduate and graduate students interested in algebra and representation theory.
Introduction
Basic notions of representation theory
General results of representation theory
Representations of finite groups: Basic results
Representations of finite groups: Further results
Quiver representations
Introduction to categories
Homological algebra
Structure of finite dimensional algebras
References for historical interludes
Bibliography
Index