Convergence and conditioning results are presented for the lowest-order member of a family of Nyström methods for arbitrary, exterior, three-dimensional Stokes flow. The flow problem is formulated in terms of a recently introduced two-parameter, weakly singular boundary integral equation of the second kind. In contrast to methods based on product integration, coordinate transformation and singu...

We use D-instantons to probe the geometry of Misner universe, and calculate the world volume field theory action, which is of the 1+0 dimensional form and highly non-local. Turning on closed string tachyons, we see from the deformed moduli space of the D-instantons that the spacelike singularity is removed and the region near the singularity becomes a fuzzy cone. The infinite past is now causal...

In this paper we present a new approach for studying the dynamics of spatially inhomogeneous cosmological models with one spatial degree of freedom. By introducing suitable scale-invariant dependent variables we write the evolution equations of the Einstein field equations as a system of autonomous partial differential equations in first-order symmetric hyperbolic format, whose explicit form de...

In AdS/CFT analyticity suggests that certain singular behaviors expected at large ’t Hooft coupling should continue smoothly to weak ’t Hooft coupling where the gauge theory is tractable. This may provide a window into stringy singularity resolution and is a promising technique for studying the signature of the black hole singularity discussed in hepth/0306170. We comment briefly on its status....

0. Introduction. A. Summary. A significant problem in topology is the classification of wild arcs in S3. The first fundamental paper in this area was written by Fox and Artin in 1948 [13]. There the authors developed rigorous algebraic means for demonstrating the nontameness of arcs. Some time later (1962) Fox and Harrold [14] succeeded in completely classifying a special class of wild arcs, th...

We compare Stein fillings and Milnor fibers for rational surface singularities with reduced fundamental cycle. Deformation theory this class of was studied by de Jong-van Straten in [dJvS98]; they associated a germ singular plane curve to each singularity described via deformations curve. consider links singularities, equipped their canonical contact structures, develop symplectic analog Strate...

Linear and nonlinear programs are often ill-posed, or approximately ill-posed. However, current commercial software often is constructed with implicit assumptions of well-posedness built in. The result is that such software returns just one of many possible solutions, without any indication that singularity or approximate singularity exists. This is illustrated by applying several commercial pa...

Disputes between evidential decision theory and causal decision theory have continued for decades, and many theorists state dissatisfaction with both alternatives. Timeless decision theory (TDT) is an extension of causal decision networks that compactly represents uncertainty about correlated computational processes and represents the decisionmaker as such a process. This simple extension enabl...

The light-like linear dilaton background represents a particularly simple timedependent 1/2 BPS solution of critical type IIA superstring theory in ten dimensions. Its lift to M-theory, as well as its Einstein frame metric, are singular in the sense that the geometry is geodesically incomplete and the Riemann tensor diverges along a light-like subspace of codimension one. We study this backgrou...


 I will describe recent joint work with Arkady Vaintrob on Fan-JarvisRuan theory, which is an analog of Gromov-Witten theory where a target space is replaced by a quasihomogeneous isolated hypersurface singularity. In the case of simple singularities of type A it corresponds to the intersection theory on the moduli space of higher spin curves, and constitutes a framework for the famous Witten ...