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We define a higher-dimensional analogue of symplectic Khovanov homology. Consider the standard Lefschetz fibration of a 2n-dimensional Milnor fiber of the A_{k-1} singularity. We represent a link by a...
It is well known that harmonic function is smoothing invariant when convolved with the standard mollifier, which gives a quick proof of the smoothness of the harmonic function. In this talk, we will c...
For each central charge c\in (0,1], we construct a conformally invariant field which is a measurable function of the local time field \mathcal{L} of the Brownian loop soup with intensity c and i.i.d. ...
In this talk, we are mainly concerned with invariant geometric flows in affine-related geometries including centro-equiane, centro-affine, affine and affine-symplectic geometries. First, we show that ...
In this talk, we will first introduce a class of Gaussian processes, and prove the quasi-invariant theorem with respect to the Gaussian Wiener measure, which is the law of the associated Gaussian proc...
Multi-temporal Earth Observation and Mars orbital imagery data with frequent repeat coverage provide great capability for planetary surface change detection. When comparing two images taken at differe...
We define Ptolemy coordinates for representations that are not necessarily boundary-unipotent. This gives rise to a new algorithm for computing the SL(2; C) Apolynomial, and more generally the ...
We give an e ient simpli ial formula for the volume and ChernSimons invariant of a boundary-paraboli PSL(2,C)representation of a tame 3manifold
With the availability of very high resolution multispectral imagery from sensors such as IKONOS and Quickbird, it is possible to identify small-scale features in urban environment. Because of the mu...
An important approach to establishing stochastic behavior of dynamical systems is based on the study of systems expanding a foliation and of measures having smooth densities along the leaves of this ...
An important discovery of the 20th century mathematics is that many deterministic systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
This paper applies the authors’ forthcoming work, ”Affine deformations of a three-holed sphere” in Lorentzian geometry to prove a result in hyperbolic geometry. Namely, an innitesimal de...
Let E denote an a±ne space modelled on Minkowski (2+1)-space E and let ¡ be a group of isometries whose linear part L(¡) is a purely hyperbolic subgroup of SO0 (2;1). Margulis has deˉned ...
In [7] it wasshown that ifn isthe fundamental group ofa closed oriented surface S and Gis Lie group satisfying very general conditions, then the space Hom(n, G)/G of conjugacy classes of representat...
The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. In this paper we utilize this principle al...

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