Mathematical Surveys and Monographs, Volume: 174
228 pp; hardcover
ISBN-13: 978-0-8218-5350-4
Expected publication date is June 10, 2011.
The direct sum behaviour of its projective modules is a fundamental property of any ring. Hereditary Noetherian prime rings are perhaps the only noncommutative Noetherian rings for which this direct sum behaviour (for both finitely and infinitely generated projective modules) is well-understood, yet highly nontrivial.
This book surveys material previously available only in the research literature. It provides a re-worked and simplified account, with improved clarity, fresh insights and many original results about finite length modules, injective modules and projective modules. It culminates in the authors' surprisingly complete structure theorem for projective modules which involves two independent additive invariants: genus and Steinitz class. Several applications demonstrate its utility.
The theory, extending the well-known module theory of commutative Dedekind domains and of hereditary orders, develops via a detailed study of simple modules. This relies upon the substantial account of idealizer subrings which forms the first part of the book and provides a useful general construction tool for interesting examples.
The book assumes some knowledge of noncommutative Noetherian rings, including Goldie's theorem. Beyond that, it is largely self-contained, thanks to the appendix which provides succinct accounts of Artinian serial rings and, for arbitrary rings, results about lifting direct sum decompositions from finite length images of projective modules. The appendix also describes some open problems.
Graduate students and research mathematicians interested in algebra, in particular, noncommutative rings
MSRI Mathematical Circles Library, Volume: 3
2011; approx. 205 pp; softcover
ISBN-13: 978-0-8218-5362-7
Expected publication date is June 26, 2011.
This geometry book is written foremost for future and current middle school teachers, but is also designed for elementary and high school teachers. The book consists of ten seminars covering in a rigorous way the fundamental topics in school geometry, including all of the significant topics in high school geometry. The seminars are crafted to clarify and enhance understanding of the subject. Concepts in plane and solid geometry are carefully explained, and activities that teachers can use in their classrooms are emphasized. The book draws on the pictorial nature of geometry since that is what attracts students at every level to the subject. The book should give teachers a firm foundation on which to base their instruction in the elementary and middle grades. In addition, it should help teachers give their students a solid basis for the geometry that they will study in high school. The book is also intended to be a source for problems in geometry for enrichment programs such as Math Circles and Young Scholars.
Undergraduate students interested in secondary education, particularly the teaching of geometry, and current middle school teachers teaching geometry.
Seminar 1: Polygons in the plane
Seminar 2: More fundamentals of plane geometry
Seminar 3: Tessellation
Seminar 4: Regular polygons and regular polyhedra
Seminar 5: Symmetry
Seminar 6: Lattice polygons
Seminar 7: The area of polygonal regions
Seminar 8: The area of a disk and disk packing
Seminar 9: Dissection
Seminar 10: Geometry in three dimensions
Index
Clay Mathematics Proceedings, Volume: 13
2011; 647 pp; softcover
ISBN-13: 978-0-8218-5204-0
Expected publication date is June 24, 2011.
This volume constitutes the proceedings of a conference, "On Certain L-functions", held July 23-27, 2007 at Purdue University, West Lafayette, Indiana. The conference was organized in honor of the 60th birthday of Freydoon Shahidi, widely recognized as having made groundbreaking contributions to the Langlands program.
The articles in this volume represent a snapshot of the state of the field from several viewpoints. Contributions illuminate various areas of the study of geometric, analytic, and number theoretic aspects of automorphic forms and their L-functions, and both local and global theory are addressed.
Topics discussed in the articles include Langlands functoriality, the Rankin-Selberg method, the Langlands-Shahidi method, motivic Galois groups, Shimura varieties, orbital integrals, representations of p-adic groups, Plancherel formula and its consequences, the Gross-Prasad conjecture, and more. The volume also includes an expository article on Shahidi's contributions to the field, which serves as an introduction to the subject.
Experts will find this book a useful reference, and beginning researchers will be able to use it to survey major results in the Langlands program.
Graduate students and research mathematicians interested in analytic number theory and automorphic forms.
S. Gelbart -- Shahidi's work "On certain L-functions": A short history of Langlands-Shahidi theory
J. Arthur -- The embedded eigenvalue problem for classical groups
M. Asgari and A. Raghuram -- A cuspidality criterion for the exterior square transfer of cusp forms on GL(4)
C. J. Bushnell, G. Henniart, and P. C. Kutzko -- Types and explicit Plancherel formulae for reductive p-adic groups
B. Casselman -- Jacquet modules and the asymptotic behaviour of matrix coefficients
L. Clozel -- The ABS principle: Consequences for L^2(G/H)
L. Clozel and J.-P. Labesse -- Orbital integrals and distributions
J. W. Cogdell, I. I. Piatetski-Shapiro, and F. Shahidi -- Functoriality for the quasisplit classical groups
D. Ginzburg, D. Jiang, and D. Soudry -- Poles of L-functions and theta liftings for orthogonal groups, II
D. Goldberg -- On dual R-groups for classical groups
H. Hida -- Irreducibility of the Igusa tower over unitary Shimura varieties
H. Jacquet and S. Rallis -- On the Gross-Prasad conjecture for unitary groups
H. H. Kim and W. Kim -- On local L-functions and normalized intertwining operators II; Quasi-split groups
R. P. Langlands -- Reflexions on receiving the Shaw Prize
E. Lapid -- On Arthur's asymptotic inner product formula of truncated Eisenstein series
C. Moeglin -- Multiplicite 1 dans les paquets d'Arthur aux places p-adiques
G. Mui? and M. Tadi? -- Unramified unitary duals for split classical p-adic groups; The topology and isolated representations
F. Murnaghan -- Parametrization of tame supercuspidal representations
V. K. Murty -- On the Sato-Tate conjecture, II
D. Ramakrishnan -- Icosahedral fibres of the symmetric cube and algebraicity
J. Rohlfs and B. Speh -- Pseudo Eisenstein forms and the cohomology of arithmetic groups III: Residual cohomology classes
P. Schneider and M.-F. Vigneras -- A functor from smooth o-torsion representations to (\varphi,\Gamma)-modules
H. Yoshida -- Motivic Galois groups and L-groups
Contemporary Mathematics, Volume: 544
2011; 159 pp; softcover
ISBN-13: 978-0-8218-5259-0
Expected publication date is June 26, 2011.
This volume contains the proceedings of the Seventh Workshop in Lie Theory and Its Applications, which was held November 27-December 1, 2009 at the Universidad Nacional de Cordoba, in Cordoba, Argentina. The workshop was preceded by a special event, "Encuentro de teoria de Lie", held November 23-26, 2009, in honor of the sixtieth birthday of Jorge A. Vargas, who greatly contributed to the development of Lie theory in Cordoba.
This volume focuses on representation theory, harmonic analysis in Lie groups, and mathematical physics related to Lie theory. The papers give a broad overview of these subjects and also of the recent developments of the authors' research.
Graduate students and research mathematicians interested in Lie theory and its applications.
F. Levstein, C. Maldonado, and D. Penazzi -- Lattices, frames and Norton algebras of dual polar graphs
J. Faraut -- Asymptotic spherical analysis
J. Vargas -- Restriction of discrete series of a semisimple Lie group to reductive subgroups
S. Dann and G. Olafsson -- Paley-Wiener theorems with respect to the spectral parameter
G. Olafsson and J. A. Wolf -- Extension of symmetric spaces and restriction of Weyl groups and invariant polynomials
A. H. Dooley -- Intertwining operators, the Cayley transform, and the contraction of K to NM
L. Gutierrez, J. Pantoja, and J. Soto-Andrade -- On generalized Weil representations over involutive rings
N. Andruskiewitsch, I. Angiono, and H. Yamane -- On pointed Hopf superalgebras
V. Serganova -- Quasireductive supergroups
Contemporary Mathematics, Volume: 545
2011; 211 pp; softcover
ISBN-13: 978-0-8218-4971-2
Expected publication date is July 16, 2011.
The volume contains the proceedings of the international workshop on Concentration, Functional Inequalities and Isoperimetry, held at Florida Atlantic University in Boca Raton, Florida, from October 29-November 1, 2009.
The interactions between concentration, isoperimetry and functional inequalities have led to many significant advances in functional analysis and probability theory. Important progress has also taken place in combinatorics, geometry, harmonic analysis and mathematical physics, to name but a few fields, with recent new applications in random matrices and information theory.
Graduate students and research mathematicians interested in the interplay between analysis, probability, and geometry.
S. Aida -- COH formula and Dirichlet Laplacians on small domains of pinned path spaces
N. Badr and G. Dafni -- Maximal characterization of Hardy-Sobolev spaces on manifolds
S. G. Bobkov -- On Milman's ellipsoids and M-position of convex bodies
S. G. Bobkov, M. Madiman, and L. Wang -- Fractional generalizations of Young and Brunn-Minkowski inequalities
R. Eldan and B. Klartag -- Approximately Gaussian marginals and the hyperplane conjecture
O. N. Feldheim and S. Sodin -- One more proof of the Erd?s-Turan inequality, and an error estimate in Wigner's law
A. Figalli -- Quantitative isoperimetric inequalities with applications to the stability of liquid drops and crystals
R. L. Frank and E. H. Lieb -- Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality
A. Giannopoulos, G. Paouris, and P. Valettas -- On the existence of subgaussian directions for log-concave measures
A. V. Kolesnikov and R. I. Zhdanov -- On isoperimetric sets of radially symmetric measures
M. Ledoux -- From concentration to isoperimetry: Semigroup proofs
J. Martin and M. Milman -- Sobolev inequalities, rearrangements, isoperimetry and interpolation spaces
E. Milman -- Isoperimetric bounds on convex manifolds
F. Morgan -- The log-convex density conjecture
Student Mathematical Library, Volume: 60
2011; approx. 312 pp; softcover
ISBN-13: 978-0-8218-5368-9
Expected publication date is August 17, 2011.
This book presents a number of topics related to surfaces, such as Euclidean, spherical and hyperbolic geometry, the fundamental group, universal covering surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. The main idea is to get to some interesting mathematics without too much formality. The book also includes some material only tangentially related to surfaces, such as the Cauchy Rigidity Theorem, the Dehn Dissection Theorem, and the Banach-Tarski Theorem.
The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis.
Undergraduate students interested in geometry and topology of surfaces.
Book overview
Definition of a surface
The gluing construction
The fundamental group
Examples of fundamental groups
Covering spaces and the deck group
Existence of universal covers
Euclidean geometry
Spherical geometry
Hyperbolic geometry
Riemann metrics on surfaces
Hyperbolic surfaces
A primer on complex analysis
Disk and plane rigidity
The Schwarz-Christoffel transformation
Riemann surfaces and uniformization
Flat cone surfaces
Translation surfaces and the Veech group
Continued fractions
Teichmuller space and moduli space
Topology of Teichmuller space
The Banach Tarski theorem
Dehn's dissection theorem
The Cauchy rigidity theorem
Bibliography
Index