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In a recent paper, M. Green and P. Griths used R. Thomas’ work on nodal hypersurfaces to sketch a proof of the equivalence of the Hodge conjecture and the existence of certain singular admissible no...
We show that the zero locus of a normal function on a smooth complex algebraic variety S is algebraic provided that the normal function extends to a admissible normal function on a smooth compacti...
Statement of the main result. We study a two-center two-body problem. Consider two xed centers Q1 and Q2 of masses m1 = m2 = 1 located at distance from each other and two small particles Q3 and Q4...
In this paper, we first derive a pinching estimate on the traceless Ricci curvature in term of scalar curvature and Weyl tensor under the Ricci flow. Then we apply this estimate to study...
This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges.Conceptually, the curvelet transfo...
Singularities of generic mean curvature flow.
We show that "splash" singularities cannot develop in the case of locally smooth solutions of the two-uid interfaces in two dimensions. More precisely, we show that the scenario of formation of singul...
An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volu...
We develop an adaptive edgeite element method based on reliable and e眂ient residual-based a posteriori error estimates for low-frequency time-harmonic Maxwell's equations with singularities. The r...
In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. A generalization of the local {\delta}-inv...
We provide an alternative proof of the classical single-term asymptotics for Toeplitz determinants whose symbols possess Fisher-Hartwig singularities. We also relax the smoothness conditions on the re...
Let $X$ be a smooth irreducible nondegenerate projective variety and let $X^*$ denote its dual variety. It is well known that $\sigma_2(X)^*$, the dual of the 2-secant variety of $X$, is a component o...
We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence o...
In a previous work we have introduced and studied the notion of embedded $\mathbf{Q}$-resolution, which essentially consists in allowing the final ambient space to contain abelian quotient singulariti...

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