arXiv
(422,153 recursos)
This is one of the most extensive subject based repositories in the world in the field of physics, mathematics, astronomy, computer sciences and quantitative biology. This is the principal site with almost 20 mirror versions around the globe. The site is supported by an extensive collection of information and background documentation. An RSS feed is available for anyone interested in keeping up-to-date with newly added materials.
Mostrando recursos 81 - 100 de 66,283
81.
Emerging applications of geometric multiscale analysis - Donoho, David L.
Classical multiscale analysis based on wavelets has a number of successful
applications, e.g. in data compression, fast algorithms, and noise removal.
Wavelets, however, are adapted to point singularities, and many phenomena in
several variables exhibit intermediate-dimensional singularities, such as
edges, filaments, and sheets. This suggests that in higher dimensions, wavelets
ought to be replaced in certain applications by multiscale analysis adapted to
intermediate-dimensional singularities.
My lecture described various initial attempts in this direction. In
particular, I discussed two approaches to geometric multiscale analysis
originally arising in the work of Harmonic Analysts Hart Smith and Peter Jones
(and others): (a) a directional wavelet transform based on parabolic dilations;
and (b) analysis...
82.
Algebraic topology and modular forms - Hopkins, Michael J.
Modular forms appear in many facets of mathematics, and have played important
roles in geometry, mathematical physics, number theory, representation theory,
topology, and other areas. Around 1994, motivated by technical issues in
homotopy theory, Mark Mahowald, Haynes Miller and I constructed a topological
refinement of modular forms, which we call {\em topological modular forms}. At
the Zurich ICM I sketched a program designed to relate topological modular
forms to invariants of manifolds, homotopy groups of spheres, and ordinary
modular forms. This program has recently been completed and new directions have
emerged. In this talk I will describe this recent work and how it informs our
understanding of both algebraic...
83.
Some highlights of percolation - Kesten, Harry
We describe the percolation model and some of the principal results and open
problems in percolation theory. We also discuss briefly the spectacular recent
progress by Lawler, Schramm, Smirnov and Werner towards understanding the phase
transition of percolation (on the triangular lattice).
84.
Geometric construction of representations of affine algebras - Nakajima, Hiraku
Let $\Gamma$ be a finite subgroup of $\SL_2(\C)$. We consider $\Gamma$-fixed
point sets in Hilbert schemes of points on the affine plane $\C^2$. The direct
sum of homology groups of components has a structure of a representation of the
affine Lie algebra $\ag$ corresponding to $\Gamma$. If we replace homology
groups by equivariant $K$-homology groups, we get a representation of the
quantum toroidal algebra $\Ut$. We also discuss a higher rank generalization
and character formulas in terms of intersection homology groups.
85.
Some recent transcendental techniques in algebraic and complex geometry - Siu, Yum-Tong
This article discusses the recent transcendental techniques used in the
proofs of the following three conjectures. (1)~The plurigenera of a compact
projective algebraic manifold are invariant under holomorphic deformation.
(2)~There exists no smooth Leviflat hypersurface in the complex projective
plane. (3)~A generic hypersurface of sufficiently high degree in the complex
projective space is hyperbolic in the sense that there is no nonconstant
holomorphic map from the complex Euclidean line to it.
86.
Galois representations - Taylor, Richard
In the first part of this paper we try to explain to a general mathematical
audience some of the remarkable web of conjectures linking representations of
Galois groups with algebraic geometry, complex analysis and discrete subgroups
of Lie groups. In the second part we briefly review some limited recent
progress on these conjectures.
87.
Geometry and nonlinear analysis - Tian, Gang
Nonlinear analysis has played a prominent role in the recent developments in
geometry and topology. The study of the Yang-Mills equation and its cousins
gave rise to the Donaldson invariants and more recently, the Seiberg-Witten
invariants. Those invariants have enabled us to prove a number of striking
results for low dimensional manifolds, particularly, 4-manifolds. The theory of
Gromov-Witten invariants was established by using solutions of the
Cauchy-Riemann equation. These solutions are often refered as
pseudo-holomorphic maps which are special minimal surfaces studied long in
geometry. It is certainly not the end of applications of nonlinear partial
differential equations to geometry. In this talk, we will discuss some recent
progress on...
88.
The power set function - Gitik, Moti
We survey old and recent results on the problem of finding a complete set of
rules describing the behavior of the power function, i.e. the function which
takes a cardinal $\kappa$ to the cardinality of its power $2^\kappa$.
89.
Beyond $\underTilde{\Sigma}^2_1$ absoluteness - Woodin, W. Hugh
There have been many generalizations of Shoenfield's Theorem on the
absoluteness of $\Sigma^1_2$ sentences between uncountable transitive models of
$\mathrm{ZFC}$. One of the strongest versions currently known deals with
$\Sigma^2_1$ absoluteness conditioned on $\mathrm{CH}$. For a variety of
reasons, from the study of inner models and from simply combinatorial set
theory, the question of whether conditional $\Sigma^2_2$ absoluteness is
possible at all, and if so, what large cardinal assumptions are involved and
what sentence(s) might play the role of $\mathrm{CH}$, are fundamental
questions. This article investigates the possiblities for $\Sigma^2_2$
absoluteness by extending the connections between determinacy hypotheses and
absoluteness hypotheses.
90.
Evolution of curves and surfaces by mean curvature - White, Brian
This article describes the mean curvature flow, some of the discoveries that
have been made about it, and some unresolved questions.
91.
On Hrushovski's proof of the Manin-Mumford conjecture - Pink, Richard; Roessler, Damian
The Manin-Mumford conjecture in characteristic zero was first proved by
Raynaud. Later, Hrushovski gave a different proof using model theory. His main
result from model theory, when applied to abelian varieties, can be rephrased
in terms of algebraic geometry. In this paper we prove that intervening result
using classical algebraic geometry alone. Altogether, this yields a new proof
of the Manin-Mumford conjecture using only classical algebraic geometry.
93.
Statistical equivalence and stochastic process limit theorems - Brown, Lawrence D.
A classical limit theorem of stochastic process theory concerns the sample
cumulative distribution function (CDF) from independent random variables. If
the variables are uniformly distributed then these centered CDFs converge in a
suitable sense to the sample paths of a Brownian Bridge. The so-called
Hungarian construction of Komlos, Major and Tusnady provides a strong form of
this result. In this construction the CDFs and the Brownian Bridge sample paths
are coupled through an appropriate representation of each on the same
measurable space, and the convergence is uniform at a suitable rate.
Within the last decade several asymptotic statistical-equivalence theorems
for nonparametric problems have been proven, beginning with Brown...
94.
Ergodicity and mixing for stochastic partial differential equations - Bricmont, Jean
Recently, a number of authors have investigated the conditions under which a
stochastic perturbation acting on an infinite dimensional dynamical system,
e.g. a partial differential equation, makes the system ergodic and mixing. In
particular, one is interested in finding minimal and physically natural
conditions on the nature of the stochastic perturbation. I shall review recent
results on this question; in particular, I shall discuss the Navier-Stokes
equation on a two dimensional torus with a random force which is white noise in
time, and excites only a finite number of modes. The number of excited modes
depends on the viscosity $\nu$, and grows like $\nu^{-3}$ when $\nu$ goes to
zero....
95.
Smoothed analysis of algorithms - Spielman, Daniel A.; Teng, Shang-Hua
Spielman and Teng introduced the smoothed analysis of algorithms to provide a
framework in which one could explain the success in practice of algorithms and
heuristics that could not be understood through the traditional worst-case and
average-case analyses. In this talk, we survey some of the smoothed analyses
that have been performed.
96.
Adaptive methods for PDE's: wavelets or mesh refinement? - Cohen, Albert
Adaptive mesh refinement techniques are nowadays an established and powerful
tool for the numerical discretization of PDE's. In recent years, wavelet bases
have been proposed as an alternative to these techniques. The main motivation
for the use of such bases in this context is their good performances in data
compression and the approximation theoretic foundations which allow to analyze
and optimize these performances. We shall discuss these theoretical
foundations, as well as one of the approaches which has been followed in
developing efficient adaptive wavelet solvers. We shall also discuss the
similarities and differences between wavelet methods and adaptive mesh
refinement.
97.
Energy landscapes and rare events - E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
Many problems in physics, material sciences, chemistry and biology can be
abstractly formulated as a system that navigates over a complex energy
landscape of high or infinite dimensions. Well-known examples include phase
transitions of condensed matter, conformational changes of biopolymers, and
chemical reactions. The energy landscape typically exhibits multiscale
features, giving rise to the multiscale nature of the dynamics. This is one of
the main challenges that we face in computational science. In this report, we
will review the recent work done by scientists from several disciplines on
probing such energy landscapes. Of particular interest is the analysis and
computation of transition pathways and transition rates between metastable
states. We...
98.
International comparisons in mathematics education: an overview - Kaiser, Gabriele; Leung, Frederick K. S.; Romberg, Thomas; Yaschenko, Ivan
The paper opens with an overview of the discussion of international
comparisons (including goals) in mathematics education. Afterwards, the two
most important recent international studies, the PISA Study and TIMSS-Repeat,
are described. After a short description of the qualitative-quantitative
debate, a qualitatively oriented small-scale study is described. The paper
closes with reflection on the possibilities and limitations of such studies.
99.
The work of Laurent Lafforgue - Laumon, Gérard
Laurent Lafforgue has been awarded the Fields Medal for his proof of the
Langlands correspondence for the full linear groups $\mathop{\rm
GL}\nolimits_{r}$ ($r\geq 1$) over function fields.
This article is a brief introduction to the Langlands correspondence and to
Lafforgue's theorem.
100.
The work of Vladimir Voevodsky - Soulé, Christophe
Vladimir Voevodsky was born in 1966. He studied at Moscow State University
and Harvard university. He is now Professor at the Institute for Advanced Study
in Princeton.
Among his main achievements are the following: he defined and developed
motivic cohomology and the ${\mathbf A}^1$-homotopy theory of algebraic
varieties; he proved the Milnor conjectures on the $K$-theory of fields. This
article is a brief introduction to this work, for which Voevodsky was awarded
the Fields Medal.
81.
