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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 ...
PTOLEMY COORDINATES, DEHN INVARIANT AND THE A-POLYNOMIAL     A-POLYNOMIAL  DEHN INVARIANT       font style='font-size:12px;'> 2015/12/17
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 ...
THE VOLUME AND CHERNSIMONS INVARIANT OF A REPRESENTATION     VOLUME  CHERNSIMONS INVARIANT       font style='font-size:12px;'> 2015/12/17
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
AVERAGING AND INVARIANT MEASURES     AVERAGING AND INVARIANT MEASURES  Power system       font style='font-size:12px;'> 2015/9/29
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...
Stretching Three-Holed Spheres and the Margulis Invariant     Margulis Invariant  Three-Holed Spheres       font style='font-size:12px;'> 2015/9/29
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...
Normally hyperbolic invariant manifolds near strong double resonance.
In this paper we study existence of Normally Hyperbolic Invariant Laminations (NHIL) for a nearly integrable system given by the product of the pendulum and the rotator perturbed with a small coupling...
We combine the technique of inducing with a method of Johnson boxes and construct new examples of S-unimodal maps ϕ which do not have a finite absolutely continuous invariant measure, but do have...

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