ISBN: 978-1-57146-140-7
Published: 15 April 2010; Copyright Year: 2010; Pages: 407; Hardcover
Graduate students and research mathematicians interested in geometry.
The editors of the highly esteemed Journal of Differential Geometry (published
by International Press) each year present a new volume of Surveys in Differential
Geometry, a collection of original contributions upon a specially chosen
topic pertaining to differential geometry and related topics.
The series presents an overview of recent trends, while making predictions and suggestions for future research.
Each invited contributor is a prominent specialist in the field of algebraic
geometry, mathematical physics, or related areas. Contributors to Surveys
tend to transcend classical frameworks within their field.
Once every three years, Lehigh University and Harvard University, in conjunction
with the editors of the JDG, sponsor a conference whose purpose is to survey
the general field of differential geometry and related subjects. Speakers
at the conference are likewise selected for their prominence in a given
field and for their innovative contributions to it. Hence every third volume
of Surveys is a publication of those presented talks.
The Surveys in Differential Geometry series is a beneficial collection
for experts and non-experts alike, and in particular, for those independent
of the mainstream of activity in the field of geometry.
E. Arbarello and M. Cornalba -- Divisors in the moduli spaces of curves
R. L. Cohen -- Stability phenomena in the topology of moduli spaces
G. Farkas -- Birational aspects of the geometry of M_g
S. Grushevsky and I. Krichever -- The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces
J. Harris -- Brill-Noether theory
P. Hubert, E. Lanneau, and M. Moller -- GL{^+}{_2}(R)-orbit closures via topological splittings
J. Jost and S. T. Yau -- Harmonic mappings and moduli spaces of Riemann surfaces
Y.-P. Lee and R. Vakil -- Algebraic structures on the topology of moduli spaces of curves and maps
K. Liu, X. Sun, and S.-T. Yau -- Recent development on the geometry of the Teichmuller and moduli spaces of Riemann surfaces
V. Markovic -- The universal properties of Teichmuller spaces
H. Masur -- Geometry of Teichmuller space with the Teichmuller metric
I. Morrison -- GIT constructions of moduli spaces of stable curves and maps
Y. Ruan -- Riemann surfaces, integrable hierarchies, and singularity theory
ISBN: 978-1-57146-199-5
Published: 15 April 2010; Copyright Year: 2010; Pages: 154; Softcover
Graduate students and research mathematicians interested in geometry and topology.
The Gokova Geometry-Topology Conferences were inaugurated in 1992 with
the support of TUBITAK (The Scientific and Technological Research Council
of Turkey) and are held annually on the shores of the scenic Gokova Bay
on the southwestern coast of Turkey.
These conferences have been supported by TUBITAK since their inception
and since 2005 they have received partial funding from NSF. Over the years
the topics of these conferences were chosen from the exciting subjects
of geometry and topology, usually with the most recent developments taking
the front stage.
W. Chen -- Group actions on 4-manifolds: Some recent results and open questions
M. Shapiro -- Introduction to integrable systems: Open Toda lattice, KP-, and KdV-hierarchies
P. Rossi -- Integrable systems and holomorphic curves
F. Catanese, M. Lonne, and B. Wajnryb -- Moduli spaces of surfaces and monodromy invariants
S. Salur and A. J. Todd -- Deformations of asymptotically cylindrical special Lagrangian submanifolds
J. Fine and D. Panov -- Building symplectic manifolds using hyperbolic geometry
S. Akbulut -- Twisting 4-manifolds along RP^2
ISBN: 978-0-8218-5166-1
Published: 13 October 2010; Copyright Year: 2010; Pages: 218; Softcover
Undergraduates, graduate students, and research mathematicians interested in the life and work of a remarkable mathematician and physicist.
The Intrinsic Nature of Things is the extraordinary story of the Hungarian-born
mathematician and physicist Cornelius Lanczos. His deep awareness of the
beauty in science, encapsulated in his phrase gscience as a kind of arth,
informed both his life and his work. Gellaifs biography of Lanczos analyzes
how the social and historical circumstances around him- in Hungary, Germany,
the United States, and Ireland-affected his career. Alongside his personal
life, and in terms that can be appreciated by professionals and laymen
alike, the author presents accounts of his mathematical accomplishments
and his novel ideas in physics.
Cornelius Lanczos was a remarkable man, a remarkable teacher, and a remarkable
scientist. He is known to physicists, engineers, numerical analysts, and
applied mathematicians, though few people are aware of the breadth and
depth of his work across several disciplines. In physics, he worked first
in general relativity and later in quantum mechanics. In mathematics, Lanczos
made important contributions in many areas: differential equations, approximations
in various contexts, the singular value decomposition, the Fast Fourier
Transform, and algorithms for finding eigenvalues of large matrices.
Born and educated in Hungary, Lanczosfs scientific career began in Germany,
including a time as Einsteinfs assistant. In reaction to the anti-Semitism
of Germany in the 1930s, Lanczos emigrated to the United States. He worked
first at Purdue, then at Boeing and the US National Bureau of Standards.
In the 1950s, McCarthyism in the US convinced Lanczos to accept Schrodingerfs
invitiation to join the Dublin Institute for Advanced Studies, where he
worked to
the end of his life.
Background
Family and basic studies
A change in our world view: The theory of relativity
Higher studies
Lanczos's early research in the theory of relativity
Contribution to quantum mechanics
Purdue beginnings
The educator
"Why mathematics?"
Ripples on the old pond's surface
The Lanczos Method
Full-time research
Nature's Pythagorean theorem
Probing Riemannian space
Epilogue
A brief professional chronology of Cornelius Lanczos
Published papers and books of Cornelius Lanczos
Bibliography
Index
ISBN: 978-0-8218-5192-0
Series: University Lecture Series, Volume 55
Published: 26 September 2010; Copyright Year: 2010; Pages: approximately 142; Softcover
Advanced undergraduates and computer science majors, graduate students, and research mathematicians
interested in complexity thory; cryptography; and pseudorandom generators.
A fresh look at the question of randomness was taken in the theory of computing:
A distribution is pseudorandom if it cannot be distinguished from the uniform
distribution by any efficient procedure. This paradigm, originally associating
efficient procedures with polynomial-time algorithms, has been applied
with respect to a variety of natural classes of distinguishing procedures.
The resulting theory of pseudorandomness is relevant to science at large
and is closely related to central areas of computer science, such as algorithmic
design, complexity theory, and cryptography.
This primer surveys the theory of pseudorandomness, starting with the general
paradigm, and discussing various incarnations while emphasizing the case
of general-purpose pseudorandom generators (withstanding any polynomial-time
distinguisher).
Additional topics include the gderandomizationh of arbitrary probabilistic
polynomial-time algorithms, pseudorandom generators withstanding space-bounded
distinguishers, and several natural notions of special-purpose pseudorandom
generators.
The primer assumes basic familiarity with the notion of efficient algorithms
and with elementary probability theory, but provides a basic introduction
to all notions that are actually used. As a result, the primer is essentially
self-contained, although the interested reader is at times referred to
other sources for more detail.
Introduction
General-purpose pseudorandom generators
Derandomization of time-complexity classes
Space-bounded distinguishers
Special purpose generators
Concluding remarks
Hashing functions
On randomness extractors
A generic hard-core predicate
Using randomness in computation
Cryptographic applications of pseudorandom functions
Some basic vomplexity classes
Bibliography
Index