Edited by: Edward Bierstone, Boris Khesin, and Askold Khovanskii, University of Toronto,
ON, Canada,
and Jerrold E. Marsden, California Institute
ofTechnology, Pasadena, CA
Description
This volume presents articles originating
from invited talks at an exciting international
conference held at The Fields Institute in
Toronto celebrating the sixtieth birthday
of the renowned mathematician, Vladimir
Arnold. Experts from the world over--including
several from "Arnold's school"--gave
illuminating talks and lively poster
sessions. The presentations focussed on Arnold's
main areas of interest: singularity theory,
the theory of curves, symmetry groups, dynamical
systems, mechanics, and
related areas of mathematics.
The book begins with notes of three lectures
by V. Arnold given in the framework of the
Institute's Distinguished Lecturer program.
The topics of the lectures are:
From Hilbert's Superposition Problem to Dynamical
Systems
Symplectization, Complexification, and Mathematical
Trinities
Topological Problems in Wave Propagation
Theory and Topological Economy Principle
in Algebraic Geometry
Arnold's three articles include insightful
comments on Russian and Western mathematics
and science. Complementing the first is Jurgen
Moser's "Recollections",
concerning some of the history of KAM theory.
Contents
V. I. Arnold -- From Hilbert's superposition
problem to dynamical systems
J. Moser -- Recollections
V. I. Arnold -- Symplectization, complexification
and mathematical trinities
V. I. Arnold -- Topological problems in wave
propagation theory and topological economy
principle in algebraic geometry
M. S. Alber, G. G. Luther, J. E. Marsden,
and J. M. Robbins -- Geometry and control
of three-wave interactions
E. Bierstone and P. D. Milman -- Standard
basis along a Samuel stratum, and implicit
differentiation
J. Damon -- A global weighted version of
Bezout's theorem
A. Degtyarev and V. Kharlamov -- Real Enriques
surfaces without real points and Enriques-Einstein-Hitchin
4-manifolds
W. Ebeling and S. M. Gusein-Zade -- On the
index of a vector field at an isolated singularity
D. G. Ebin and G. Misiolek -- The exponential
map on $\Cal{D}^s_\mu$
M. H. Freedman -- Zeldovich's neutron star
and the prediction of magnetic froth
K. Fukaya and K. Ono -- Arnold conjecture
and Gromov-Witten invariant for general symplectic
manifolds
A. Gabrielov -- Multiplicity of a zero of
an analytic function on a trajectory of a
vector field
A. B. Givental -- Singularity theory and
symplectic topology
V. V. Goryunov and S. K. Lando -- On enumeration
of meromorphic functions on the line
H. Hofer and E. Zehnder -- Pseudoholomorphic
curves and dynamics
Yu. S. Ilyashenko and V. Yu. Kaloshin --
Bifurcation of planar and spatial polycycles:
Arnold's program and its development
V. M. Kharlamov, S. Yu. Orevkov, and E. I.
Shustin -- Singularity which has no $M$-smoothing
B. Khesin and A. Rosly -- Symplectic geometry
on moduli spaces of holomorphic bundles over
complex surfaces
A. Khovanskii -- Newton polyhedra, a new
formula for mixed volume, product of roots
of a system of equations
W. F. Langford and K. Zhan -- Interactions
of Andronov-Hopf and Bogdanov-Takens bifurcations
E. Mukhin and A. Varchenko -- Solutions of
the qKZB equation in tensor products of finite
dimensional modules over the elliptic quantum
group $E_{\tau,\eta}sl_2$
S. P. Novikov -- Schrodinger operators on
graphs and symplectic geometry
M. Rudnev and S. Wiggins -- On the dominant
Fourier modes in the series associated with
separatrix splitting for an a-priori stable,
three degree-of-freedom
Hamiltonian system
V. A. Vassiliev -- Homology of $i$-connected
graphs and invariants of knots, plane arrangements,
etc.
V. A. Vladimirov and K. I. Ilin -- On Arnold's
variational principles in fluid mechanics
S. Yakovenko -- On functions and curves defined
by ordinary differential equations
Y. Yomdin -- Global finiteness properties
of analytic families and algebra of their
Taylor coefficients
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Fields Institute Communications,
Volume: 24
Publication Year: 1999
ISBN: 0-8218-0945-8
Paging: 555 pp. Binding: Hardcover
--------------------------------------------------------------------------------
Edited by: Lawrence Wasson Baggett, University of Colorado, Boulder, CO,
and David Royal Larson, Texas A & M
University, College Station, TX
Description
Over the past decade, wavelets and frames
have emerged as increasingly powerful tools
of analysis on $n$-dimension Euclidean space.
Both wavelets and frames were
studied initially by using classical Fourier
analysis. However, in recent years more abstract
tools have been introduced, for example,
from operator theory, abstract
harmonic analysis, von Neumann algebras,
etc.
The editors of this volume organized a Special
Session on the functional and harmonic analysis
of wavelets at the San Antonio (TX) Joint
Mathematics Meetings. The goal
of the session was to focus research attention
on these newly-introduced tools and to share
the organizers' view that this modern application
holds the promise of
providing some deeper understanding and fascinating
new structures in pure functional analysis.
This volume presents the fruitful results
of the lively discussions that took
place at the conference.
Contents
A. Aldroubi and P. Basser -- Reconstruction
of vector and tensor fields from sampled
discrete data
L. W. Baggett and K. D. Merrill -- Abstract
harmonic analysis and wavelets in $\Bbb{R}^n$
R. Balan -- Density and redundancy of the
noncoherent Weyl-Heisenberg superframes
J. J. Benedetto and M. T. Leon -- The construction
of multiple dyadic minimally supported frequency
wavelets on $\Bbb{R}^d$
L. Brandolini, G. Garrig?s, Z. Rzeszotnik,
and G. Weiss -- The behaviour at the origin
of a class of band-limited wavelets
O. Bratteli and P. E. T. Jorgensen -- Convergence
of the cascade algorithm at irregular scaling
functions
P. G. Casazza, O. Christensen, and A. J.
E. Janssen -- Classifying tight Weyl-Heisenberg
frames
P. G. Casazza, D. Han, and D. R. Larson --
Frames for Banach spaces
J. Courter -- Construction of dilation-$d$
wavelets
M. Frank and D. R. Larson -- A module frame
concept for Hilbert C*-modules
J. Gasch and J. E. Gilbert -- Triangularization
of Hankel operators and the bilinear Hilbert
transform
R. F. Gundy -- Two remarks concerning wavelets:
Cohen's criterion for low-pass filters and
Meyer's theorem on linear independence
D. Han, D. R. Larson, M. Papadakis, and Th.
Stavropoulos -- Multiresolution analyses
of abstract Hilbert spaces and wandering
subspaces
G. Strang, V. Strela, and D.-X. Zhou -- Compactly
supported refinable functions with infinite
masks
E. Weber -- Applications of the wavelet multiplicity
function
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Contemporary Mathematics, Volume:
247
Publication Year: 1999
ISBN: 0-8218-1957-7
Paging: 308 pp. Binding: Softcover
--------------------------------------------------------------------------------
Edited by: Ya. Eliashberg, Stanford University,
CA, D. Fuchs, University of California,
Davis, CA, T. Ratiu, Ecole Polytechnique
Federale de Lausanne, Switzerland,
and A. Weinstein, University of California,
Berkeley, CA
Description
This seminar was established to encourage
ongoing interaction between geometers at
Stanford University and the University of
California (Berkeley, Davis, and Santa
Cruz). Over the years, lectures presented
have provided a panorama of developments
in symplectic and contact geometry and topology,
Poisson geometry, quantization
theory, and applications.
This volume includes papers by several of
the distinguished seminar participants. The
diversity of the topics from the seminar
are reflected in the informative
presentations. A wide range of topics are
presented in the book, including symplectic
topology, Hamiltonian dynamics, quantum cohomology
and mirror symmetry,
infinite-dimensional symplectic geometry,
the theory of Hamiltonian group actions,
and quantization.
Contents
A. Cannas da Silva and V. Guillemin -- Quantization
of symplectic orbifolds and group actions
S. K. Donaldson -- Symmetric spaces, Kahler
geometry and Hamiltonian dynamics
V. L. Ginzburg -- Hamiltonian dynamical systems
without periodic orbits
A. Givental -- The mirror formula for quintic
threefolds
F. Lalonde and C. Pestieau -- Stabilisation
of symplectic inequalities and applications
D. McDuff -- The virtual moduli cycle
R. Montgomery -- Engel deformations and contact
structures
M. Pozniak -- Floer homology, Novikov rings
and clean intersections
Y. Ruan -- Surgery, quantum cohomology and
birational geometry
D. A. Salamon -- Quantum products for mapping
tori and the Atiyah-Floer conjecture
P. Seidel -- On the group of symplectic automorphisms
of $\Bbb{C}P^m \times \Bbb{C}P^n$
S. Tolman and J. Weitsman -- On the cohomology
rings of Hamiltonian $T$-spaces
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: American Mathematical Society Translations--Series
2,
Subseries: Advances in the Mathematical Sciences
Volume: 196
Publication Year: 1999
ISBN: 0-8218-2075-3
Paging: 258 pp. Binding: Hardcover
--------------------------------------------------------------------------------
Edited by: Vladimir Arnold, University of
Paris IX, France,
Maxim Kontsevich, IHES, Bures-sur-Yvette,
France,
and Anton Zorich, University of Rennes I,
France
Description
This volume offers an account of the present
state of the art in pseudoperiodic topology--a
young branch of mathematics, born at the
boundary between the ergodic
theory of dynamical systems, topology, and
number theory. Related topics include the
theory of algorithms, convex integer polyhedra,
Morse inequalities, real algebraic
geometry, statistical physics, and algebraic
number theory. The book contains many new
results. Most of the articles contain brief
surveys on the topics, making the
volume accessible to a broad audience.
From the Preface by V.I. Arnold: "The
authors ... have done much to show how modern
mathematics begets, from this sea of pathological
counterexamples,
remarkable general and universal laws, whose
discovery would be unthinkable and whose
formulation would be impossible in the naive
set-theoretical setting."
Contents
S. M. Gusein-Zade -- On the topology of quasiperiodic
functions
M. L. Kontsevich and Yu. M. Suhov -- Statistics
of Klein polyhedra and multidimensional continued
fractions
A. Pajitnov -- $C^0$-generic properties of
boundary operators in the Novikov complex
D. A. Panov -- Pseudoperiodic mappings
A. Zorich -- How do the leaves of a closed
1-form wind around a surface?
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: American Mathematical Society Translations--Series
2,
Subseries: Advances in the Mathematical Sciences
Volume: 197
Publication Year: 1999
ISBN: 0-8218-2094-X
Paging: approximately 192 pp. Binding: Hardcover
--------------------------------------------------------------------------------
Edited by: Michael D. Fried, University of California, Irvine, CA
Description
This volume presents the results of the AMS-IMS-SIAM
Joint Summer Research Conference held at
the University of Washington (Seattle). The
talks were devoted to
various aspects of the theory of algebraic
curves over finite fields and its numerous
applications. The three basic themes are
the following:
1. Curves with many rational points. Several
articles describe main approaches to the
construction of such curves: the Drinfeld
modules and fiber product methods, the
moduli space approach, and the constructions
using classical curves.
2. Monodromy groups of characteristic $p$
covers. A number of authors presented the
results and conjectures related to the study
of the monodromy groups of curves
over finite fields. In particular, they study
the monodromy groups from genus $0$ covers,
reductions of covers, and explicit computation
of monodromy groups over finite
fields.
3. Zeta functions and trace formulas. To
a large extent, papers devoted to this topic
reflect the contributions of Professor Bernard
Dwork and his students. This
conference was the last attended by Professor
Dwork before his death, and several papers
inspired by his presence include commentaries
about the applications of trace
formulas and $L$-function.
The volume also contains a detailed introduction
paper by Professor Michael Fried, which helps
the reader to navigate in the material presented
in the book.
Contents
Beyond Weil bounds; Curves with many rational
points
H. Niederreiter and C. Xing -- Curve sequences
with asymptotically many rational points
Y. Ihara -- Shimura curves over finite fields
and their rational points
D. R. Hayes -- Distribution of minimal ideals
in imaginary quadratic function fields
Z. Chen -- Division points of Drinfeld modules
and special values of Weil $L$-functions
G. van der Geer and M. van der Vlugt -- Constructing
curves over finite fields with many points
by solving linear equations
A. Garcia and F. Torres -- On maximal curves
having classical Weierstrass gaps
Monodromy groups of characteristic $p$ curves
S. S. Abhyankar and P. A. Loomis -- Twice
more nice equations for nice groups
N. D. Elkies -- Linearized algebra and finite
groups of Lie type: I: Linear and symplectic
groups
P. D?bes -- Regular realization of abelian
groups with controlled ramification
M. Emsalem -- On reduction of covers of arithmetic
surfaces
L. M. Adleman and M.-D. Huang -- Function
field sieve method for discrete logarithms
over finite fields
Zeta functions and trace formulas
D. Wan -- A quick introduction to Dwork's
conjecture
A. Adolphson and S. Sperber -- On the degree
of the zeta function of a complete intersection
F. Lepr?vost -- The modular points of a genus
2 quotient of $X_0(67)$
C.-L. Chai and W.-C. W. Li -- Function fields:
Arithmetic applications
F. Chung -- Spanning trees in subgraphs of
lattices
M. Rosen -- Average rank for elliptic curves
and a conjecture of Nagao
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Contemporary Mathematics, Volume:
245
Publication Year: 1999
ISBN: 0-8218-0925-3
Paging: 226 pp. Binding: Softcover
--------------------------------------------------------------------------------
Description
This volume consists of the written presentations
of lectures given at two special sessions:
the AMS Special Session on Topology in Dynamics
(Winston-Salem, NC) and
the AMS-AWM Special Session on Geometry in
Dynamics (San Antonio, TX). Each article
concerns aspects of the topology or geometry
of dynamical systems. Topics
covered include the following: foliations
and laminations, iterated function systems,
the three-body problem, isotopy stability,
homoclinic tangles, fractal dimension, Morse
homology, knotted orbits, inverse limits,
contact structures, Grassmanians, blowups,
and continua.
New results are presented reflecting current
trends in topological aspects of dynamical
systems. The book offers a wide variety of
topics of special interest to those
working this area bridging topology and dynamical
systems.
Contents
M. Barge, J. Jacklitch, and G. Vago -- Homeomorphisms
of one-dimensional inverse limits with applications
to substitution tilings, unstable manifolds,
and tent
maps
P. Boyland -- Isotopy stability of dynamics
on surfaces
H. Bruin -- Homeomorphic restrictions of
unimodal maps
A. Clark -- Flows on solenoids are generically
not almost periodic
P. Collins -- Dynamics forced by surface
trellises
P. Duvall and J. Keesling -- The Hausdorff
dimension of the boundary of the Levy dragon
J. B. Etnyre and R. W. Ghrist -- Stratified
integrals and unknots in inviscid flows
V. L. Ginzburg and E. Kerman -- Periodic
orbits in magnetic fields in dimensions greater
than two
P. Hanus and M. Urbanski -- A new class of
positive recurrent functions
A. Illanes, S. Mac?as, and S. B. Nadler,
Jr. -- Symmetric products and $Q$-manifolds
S. R. Kaplan -- Symbolic dynamics of the
collinear three-body problem
A. Kasman -- Grassmannians, nonlinear wave
equations and generalized Schur functions
J. E. Keesling and C. Krishnamurthi -- The
similarity boundary of a self-similar set
P. Minc -- Homotopy classes of maps between
Knaster continua
M. Schwarz -- Equivalences for Morse homology
C. R. Seaquist -- More monotone open homogeneous
locally connected plane continua
C. W. Stark -- Blowup and fixed points
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Contemporary Mathematics, Volume:
246
Publication Year: 1999
ISBN: 0-8218-1958-5
Paging: 250 pp. Binding: Softcover
--------------------------------------------------------------------------------
Edited by: Naihuan Jing and Kailash C. Misra, North Carolina State University, Raleigh, NC
Description
This volume reflects the proceedings of the
International Conference on Representations
of Affine and Quantum Affine Algebras and
Their Applications held at North
Carolina State University (Raleigh). In recent
years, the theory of affine and quantum affine
Lie algebras has become an important area
of mathematical research with
numerous applications in other areas of mathematics
and physics.
Three areas of recent progress are the focus
of this volume: affine and quantum affine
algebras and their generalizations, vertex
operator algebras and their
representations, and applications in combinatorics
and statistical mechanics. Talks given by
leading international experts at the conference
offered both overviews on the
subjects and current research results. The
book nicely presents the interplay of these
topics recently occupying "center stage"
in the theory of infinite dimensional Lie
theory.
Contents
G. Benkart, S.-J. Kang, H. Lee, and D.-U.
Shin -- The polynomial behavior of weight
multiplicities for classical simple Lie algebras
and classical affine Kac-Moody
algebras
S. Berman and S. Tan -- A note on embeddings
of some Lie algebras defined by matrices
S. Berman and J. Szmigielski -- Principal
realization for the extended affine Lie algebra
of type $sl_2$ with coordinates in a simple
quantum torus with two
generators
V. Chari and N. Xi -- Monomial bases of quantized
enveloping algebras
J. Ding and B. Feigin -- Quantized W-algebra
of ${\frak sl}(2,1)$: a construction from
the quantization of screening operators
L. Dolan -- Affine algebras and non-perturbative
symmetries in superstring theory
C. Dong and K. Nagatomo -- Automorphism groups
and twisted modules for lattice vertex operator
algebras
P. Di Francesco -- Truncated meanders
E. Frenkel and N. Reshetikhin -- The $q$-characters
of representations of quantum affine algebras
and deformations of $\Cal W$-algebras
O. Foda and T. A. Welsh -- Melzer's identities
revisited
R. L. Griess, Jr. -- Automorphisms of lattice
type vertex operator algebras and variations,
a survey
G. Hatayama, A. Kuniba, M. Okado, T. Takagi,
and Y. Yamada -- Remarks on fermionic formula
N. Jing and K. C. Misra -- $q$-vertex operators
for quantum affine algebras
S. Kumar -- Homology of certain truncated
Lie algebras
J. Lepowsky -- Vertex operator algebras and
the zeta function
H. Li and S. Wang -- On $\Bbb Z$-graded associative
algebras and their $\Bbb N$-graded modules
D. J. Melville -- An $\Bbb A$-form technique
of quantum deformations
T. Miwa and Y. Takeyama -- Determinant formula
for the solutions of the quantum Knizhnik-Zamolodchikov
equation with $|q|=1$
E. Mukhin and A. Varchenko -- Functorial
properties of the hypergeometric map
T. Nakashima -- Polyhedral realizations of
crystal bases and braid-type isomorphisms
Y. Soibelman -- Meromorphic tensor categories,
quantum affine and chiral algebras I
W. Wang -- Dual pairs and infinite dimensional
Lie algebras
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Contemporary Mathematics, volume
248
Publication Year: 1999
ISBN: 0-8218-1199-1
Paging: 469 pp. Binding: Softcover
--------------------------------------------------------------------------------
Edited by: Myung-Hwan Kim, Seoul National
University, Korea, John S. Hsia, Ohio State University, Columbus,
OH,
Yoshiyuki Kitaoka, Nagoya University, Japan,
and Rainer Schulze-Pillot, Universitat des
Saarlandes, Saabrocken, Germany
Description
This volume presents the proceedings of an
international conference held at Seoul National
University (Korea). Talks covered recent
developments in diverse areas
related to the theory of integral quadratic
forms and hermitian forms, local densities,
linear relations and congruences of theta
series, zeta functions of prehomogeneous
vector spaces, lattices with maximal finite
matrix groups, globally irreducible lattices,
Mordell-Weil lattices, and more.
Articles in the volume represent expository
lectures by leading experts on recent developments
in the field. The book offers a comprehensive
introduction to the current
state of knowledge in the arithmetic theory
of quadratic forms and provides active directions
of research with new results. Topics addressed
in the volume emphasize
connections with related fields, such as
group theory, arithmetic geometry, analytic
number theory, and modular forms. The book
is an excellent introductory guide for
students as well as a rich reference source
for researchers.
Contents
J. S. Hsia -- Arithmetic of indefinite quadratic
forms
A. G. Earnest -- Universal and regular positive
quadratic lattices over totally real number
fields
W. K. Chan -- Class numbers of quaternary
quadratic forms of discriminant 4$p$
A. Khosravani -- Universal quadratic and
Hermitian forms
B. M. Kim, M.-H. Kim, and B.-K. Oh -- 2-universal
positive definite integral quinary quadratic
forms
Y. Kitaoka -- Finite arithmetic subgroups
of $GL_n$, VI
M. J?chner -- On the representation theory
of positive definite quadratic forms
T. Shioda -- Cyclotomic analogue in the theory
of algebraic equations of type $E_6, E_7,
E_8$
P. H. Tiep -- Globally irreducible lattices
B. H. Gross -- On simply-connected groups
over $\bold Z$, with $G(\bold R)$ compact
P. Calame and M. Mischler -- $F$-lattices
and genus of hermitian forms
D. G. James -- Primitive local densities
for unimodular quadratic forms
Y. Hironaka -- Local densities of hermitian
forms
D. R. Estes and K. Moon -- Form class groups
over number fields
F. Xu -- Arithmetic Springer theorem on quadratic
forms under field extensions of odd degree
A.-M. Berg? -- Classification of positive
forms having prescribed automorphisms
G. Nebe -- Construction and investigation
of lattices with matrix groups
R. Scharlau, A. Schiemann, and R. Schulze-Pillot
-- Theta series of modular, extremal, and
hermitian lattices
H. Katsurada -- Squared M?bius function for
half-integral matrices
N. Dummigan -- Theta series congruences
M. Hisasue -- On a denominator of a certain
formal power series attached to local densities
K.-i. Hashimoto -- Linear relations of theta
series attached to Eichler orders of quaternion
algebras
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Contemporary Mathematics, Volume:
249
Publication Year: 1999
ISBN: 0-8218-1949-6
Paging: approximately 299 pp. Binding: Softcover
@--------------------------------------------------------------------------------
Edited by: Nathaniel Dean and Cassandra M.
McZeal, Rice University, Houston, TX,
and Pamela J. Williams, Sandia Laboratories,
Livermore, CA
Description
This volume presents the proceedings of the
Fourth Conference for African-American Researchers
in the Mathematical Sciences held at the
Center for Research on
Parallel Computation at Rice University (Houston).
The included talks and poster presentations
offer a broad perspective to the critical
issues involving minority
participation in mathematics. The issues
explored are relevant not only to African
American researchers, but also to the mathematical
community in general.
This volume is the second published by the
AMS (see DIMACS series, volume 15) presenting
expository and research papers by distinguished
African American
mathematicians. In addition to filling the
existing gap on African American contributions
to mathematics, this book provides leadership
direction and role models for
students.
Contents
Research talks
E. A. Terry -- Finite sums and products in
Ramsey theory
P. J. Williams, A. S. El-Bakry, and R. A.
Tapia -- Computing an exact solution in interior-point
methods for linear programming
R. Moten -- Just the facts, Jack: Truths
and myths of automated theorem provers
J. E. Brown -- On the Sendov conjecture for
polynomials with real critical points
L. Billings, J. H. Curry, and V. Robins --
Chaos in relaxed Newton's method: The quadratic
case
G. M. N'guerekata -- Almost automorphic functions
and applications to abstract evolution equations
A. Fauntleroy -- Moduli of complete intersections
in weighted projective spaces
D. R. King -- Asymptotic behavior of characters
of representations of semi-simple Lie groups
Poster presentations
A. Nkwanta and N. Knox -- A note on Riordan
matrices
K. Weems -- Robustness of parameter estimates
in misspecified generalized linear mixed
models
Historical articles
R. Tapia -- Contemporary national mathematics
education issues and the civic mathematician
J. L. Houston -- A brief history of the National
Association of Mathematicians, Inc.
S. W. Williams -- Black research mathematicians
in the United States
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Contemporary Mathematics, Volume:
252
Publication Year: 1999
ISBN: 0-8218-1195-9
Paging: approximately 165 pp. Binding: Softcover
--------------------------------------------------------------------------------
Edited by: Vladimir Arnold, University of
Paris IX, France, Michael Atiyah, University
of Edinburgh, Scotland,
Peter Lax, New York University-Courant Institute,
NY,and Barry Mazur, Harvard University, Cambridge,
MA
Description
"The twentieth century has transformed
mathematics from a cottage industry run by
a few semi-amateurs into a worldwide industry
run by an army of professionals ... "
--from the Preface by M. Atiyah
This remarkable book is a celebration of
the state of mathematics at the end of the
millennium. Produced under the auspices of
the International Mathematical Union
(IMU), the volume was born as part of the
activities observing the World Mathematical
Year 2000.
The volume consists of 28 articles written
by some of the most influential mathematicians
of our time. Authors of 14 contributions
were recognized in various years by the
IMU as recipients of the Fields Medal, from
K. F. Roth (Fields Medalist, 1958) to W.
T. Gowers (Fields Medalist, 1998). The articles
offer valuable reflections about the
amazing mathematical progress we have witnessed
in this century and insightful speculations
about the possible development of mathematics
over the next century.
Some articles formulate important problems,
challenging future mathematicians. Others
pay explicit homage to the famous set of
Hilbert Problems posed one hundred years ago, giving enlightening commentary.
Yet other papers offer a deeply personal
perspective, allowing singular insight into
the minds and hearts of people doing
mathematics today.
Mathematics: Frontiers and Perspectives is
a unique volume that pertains to a broad
mathematical audience of various backgrounds
and levels of interest. It offers
readers true and unequaled insight into the
wonderful world of mathematics at this important
juncture: the turn of the millennium.
The work is one of those rare volumes that
can be browsed, and if you do simply browse
through it, you get a wonderful sense of
mathematics today. Yet it also can be
intensely studied on a detailed technical
level for gaining insight into some of the
great problems on which mathematicians are
currently working.
Contents
A. Baker and G. W?stholz -- Number theory,
transcendence and Diophantine geometry in
the next millennium
J. Bourgain -- Harmonic analysis and combinatorics:
How much may they contribute to each other?
S.-S. Chern -- Back to Riemann
A. Connes -- Noncommutative geometry and
the Riemann zeta function
S. K. Donaldson -- Polynomials, vanishing
cycles and Floer homology
W. T. Gowers -- The two cultures of mathematics
V. F. R. Jones -- Ten problems
D. Kazhdan -- An algebraic integration
F. Kirwan -- Mathematics: The right choice?
P.-L. Lions -- On some challenging problems
in nonlinear partial differential equations
A. J. Majda -- Real world turbulence and
modern applied mathematics
Yu. I. Manin -- Mathematics as profession
and vocation
G. Margulis -- Problems and conjectures in
rigidity theory
D. McDuff -- A glimpse into symplectic geometry
S. Mori -- Rational curves on algebraic varieties
D. Mumford -- The dawning of the age of stochasticity
R. Penrose -- Mathematical physics of the
20$^{\mathrm th}$ and 21$^{\mathrm st}$ centuries
K. F. Roth -- Limitations to regularity
D. Ruelle -- Conversations on mathematics
with a visitor from outer space
P. Sarnak -- Some problems in number theory,
analysis and mathematical physics
S. Smale -- Mathematical problems for the
next century
R. P. Stanley -- Positivity problems and
conjectures in algebraic combinatorics
C. Vafa -- On the future of mathematics/physics
interaction
A. Wiles -- Twenty years of number theory
E. Witten -- Magic, mystery, and matrix
S.-T. Yau -- Review of geometry and analysis
V. I. Arnold -- Polymathematics: Is mathematics
a single science or a set of arts?
P. D. Lax -- Mathematics and computing
B. Mazur -- The theme of $p$-adic variation
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Publication Year: 2000
ISBN: 0-8218-2070-2
Paging: 459 pp. Binding: Hardcover
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