What's Happening in the Mathematical Sciences, Volume: 7
2009; 127 pp; softcover
ISBN-13: 978-0-8218-4478-6
Expected publication date is December 17, 2008.
Since 1993, the AMS has been publishing What's Happening in the Mathematical Sciences, a series of lively and highly readable accounts of the latest developments in mathematics. This seventh volume describes some genuine surprises, such as the recent discovery that coin tosses are inherently unfair; a mathematical theory of invisibility that was soon followed by the creation of a prototype "invisibility cloak"; and an ultra-efficient approach to image sensing that led to the development of a single-pixel camera.
The past few years have also seen deep results on some classical mathematics
problems. For example, this volume describes a proof of the Sato-Tate Conjecture
in number theory and a major advance in the Minimal Model Program of algebraic
geometry. The computation of the character table of the exceptional Lie
group E_8 brings "the most beautiful structure in mathematics"
to public attention, and proves that human persistence is just as important
as gigabytes of RAM. The amazing story of the Archimedes Palimpsest shows
how the modern tools of high-energy physics uncovered the centuries-old
secrets of the mathematical writings of Archimedes.
Dana Mackenzie, a science writer specializing in mathematics, makes each of these topics accessible to all readers, with a style that is friendly and at the same time attentive to the nuances that make mathematics fascinating. Anyone with an interest in mathematics, from high school teachers and college students to engineers and computer scientists, will find something of interest here. The stories are well told and the mathematics is compelling.
General mathematical audience.
Introduction
A new twist in knot theory
Error-term roulette and the Sato-Tate conjecture
The fifty-one percent solution
Dominos, anyone?
Not seeing is believing
Getting with the (Mori) program
The book that time couldn't erase
Charting a 248-dimensional world
Compressed sensing makes every pixel count
MSRI Mathematical Circles Library, Volume: 2
2009; 217 pp; softcover\
ISBN-13: 978-0-8218-4752-7
Expected publication date is February 12, 2009.
Math circles provide a setting in which mathematicians work with secondary school students who are interested in mathematics. This form of outreach, which has existed for decades in Russia, Bulgaria, and other countries, is now rapidly spreading across the United States as well. The first part of this book offers helpful advice on all aspects of math circle operations, culled from conversations with over a dozen directors of successful math circles. Topics include creative means for getting the word out to students, sound principles for selecting effective speakers, guidelines for securing financial support, and tips for designing an exciting math circle session. The purpose of this discussion is to enable math circle coordinators to establish a thriving group in which students can experience the delight of mathematical investigation. The second part of the book outlines ten independent math circle sessions, covering a variety of topics and difficulty levels. Each chapter contains detailed presentation notes along with a useful collection of problems and solutions. This book will be an indispensable resource for any individual involved with a math circle or anyone who would like to see one begin in his or her community.
Sam Vandervelde teaches at St. Lawrence University. He launched the Stanford Math Circle and also writes and coordinates the Mandelbrot Competition, a math contest for high schools.
High school teachers, college professors, and research mathematicians interested in the mathematical education of talented middle and high school students.
Fields Institute Monographs, Volume: 25
2009; 203 pp; hardcover
ISBN-13: 978-0-8218-4734-3
Expected publication date is March 11, 2009.
These lecture notes take the reader from Lennart Carleson's first deep
results on interpolation and corona problems in the unit disk to modern
analogues in the disk and ball. The emphasis is on introducing the diverse
array of techniques needed to attack these problems rather than producing
an encyclopedic summary of achievements. Techniques from classical analysis
and operator theory include duality, Blaschke product constructions, purely
Hilbert space arguments, bounded mean oscillation, best approximation,
boundedness of the Beurling transform, estimates on solutions to the \bar\partial
equation, the Koszul complex, use of trees, the complete Pick property,
and the Toeplitz corona theorem. An extensive appendix on background material
in functional analysis and function theory on the disk is included for
the reader's convenience.
Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students and research mathematicians interested in function theory in the unit disk and ball, and interpoloation and corona problems.
Preliminaries
The interpolation problem
The corona problem
Toeplitz and Hankel operators
Hilbert function spaces and Nevanlinna-Pick kernels
Carleson measures for the Hardy-Sobolev spaces
Functional analysis
Weak derivatives and Sobolev spaces
Function theory on the disk
Spectral theory for normal operators
Bibliography
Index
Proceedings of Symposia in Pure Mathematics, Volume: 80-1.
2009; approx. 492 pp; hardcover
ISBN-13: 978-0-8218-4702-2
Expected publication date is March 5, 2009.
The 2005 AMS Summer Institute on Algebraic Geometry in Seattle was an enormous event. With over 500 participants, including many of the world's leading experts, it was perhaps the largest conference on algebraic geometry ever held. These two proceedings volumes present research and expository papers by some of the most outstanding speakers at the meeting, vividly conveying the grandeur and vigor of the subject.
The most exciting topics in current algebraic geometry research receive very ample treatment. For instance, there is enlightening information on many of the latest technical tools, from jet schemes and derived categories to algebraic stacks. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties. Other papers discuss the recent dramatic advances in higher-dimensional birational geometry, while still others trace the influence of quantum field theory on algebraic geometry via mirror symmetry, Gromov-Witten invariants, and symplectic geometry.
The proceedings of earlier algebraic geometry AMS Institutes, held at Woods Hole, Arcata, Bowdoin, and Santa Cruz, have become classics. The present volumes promise to be equally influential. They present the state of the art in algebraic geometry in papers that will have broad interest and enduring value.
Graduate students and research mathematicians interested in algebraic geometry.
T. Bridgeland -- Spaces of stability conditions
J. Bryan and T. Graber -- The crepant resolution conjecture
R. L. Cohen and I. Madsen -- Surfaces in a background space and the homology of mapping class groups
I. Coskun and R. Vakil -- Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus
G. Farkas -- The global geometry of the moduli space of curves
M. Gross -- The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations
S. Grushevsky -- Geometry of \mathcal{A}_g and its compactifications
D. Huybrechts -- The global Torelli theorem: classical, derived, twisted
A. Kresch -- On the geometry of Deligne-Mumford stacks
A. Langer -- Moduli spaces of sheaves and principal G-bundles
Y.-P. Lee -- Notes on axiomatic Gromov-Witten theory and applications
A. Okounkov and R. Pandharipande -- Gromov-Witten theory, Hurwitz numbers, and matrix models
P. Seidel -- Symplectic homology as Hochschild homology
B. Toen -- Higher and derived stacks: a global overview
*
Proceedings of Symposia in Pure Mathematics, Volume: 80-2.
2009; approx. 519 pp; hardcover
ISBN-13: 978-0-8218-4703-9
Expected publication date is March 5, 2009.
The 2005 AMS Summer Institute on Algebraic Geometry in Seattle was an enormous event. With over 500 participants, including many of the world's leading experts, it was perhaps the largest conference on algebraic geometry ever held. These two proceedings volumes present research and expository papers by some of the most outstanding speakers at the meeting, vividly conveying the grandeur and vigor of the subject.
The most exciting topics in current algebraic geometry research receive very ample treatment. For instance, there is enlightening information on many of the latest technical tools, from jet schemes and derived categories to algebraic stacks. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties. Other papers discuss the recent dramatic advances in higher-dimensional birational geometry, while still others trace the influence of quantum field theory on algebraic geometry via mirror symmetry, Gromov-Witten invariants, and symplectic geometry.
The proceedings of earlier algebraic geometry AMS Institutes, held at Woods Hole, Arcata, Bowdoin, and Santa Cruz, have become classics. The present volumes promise to be equally influential. They present the state of the art in algebraic geometry in papers that will have broad interest and enduring value.
Graduate students and research mathematicians interested in algebraic geometry.
M. A. A. De Cataldo and L. Migliorini -- Hodge-theoretic aspects of the decomposition theorem
L. Ein and M. Musta?? -- Jet schemes and singularities
H. Gangl, A. B. Goncharov, and A. Levin -- Multiple polylogarithms, polygons, trees and algebraic cycles
D. Kaledin -- Geometry and topology of symplectic resolutions
S. Kaliman -- Actions of \mathbb{C}^* and \mathbb{C}_+ on affine algebraic
varieties
Y. Kawamata -- Derived categories and birational geometry
K. S. Kedlaya -- p-adic cohomology
S. A. Kovacs -- Subvarieties of moduli stacks of canonically polarized varieties: generalizations of Shafarevich's conjecture
S. J. Kovacs -- Young person's guide to moduli of higher dimensional varieties
F. Loeser -- Seattle lectures on motivic integration
M. Manetti -- Differential graded Lie algebras and formal deformation theory
M. C. Olsson -- On Faltings' method of almost etale extensions
B. Hassett and Y. Tschinkel -- Weak approximation for hypersurfaces of low degree
J. W?odarczyk -- Simple constructive weak factorization