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In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow,surface diffusion flow, Willmore flow, etc., which arise from materials science...
This talk is concerned with the controllability, observability and inverse problems for two types of stochastic partial differential equations, which are degenerate/singular stochastic parabolic equat...
We present an ordinary differential equations approach to the analysis of algorithms for constructing l1 minimizing solutions to underdeter mined linear systems of full rank. It involves a relaxed min...
We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical sing...
Abstract: In this paper we study some weighted isoperimetric inequalities relative to cones of $\mathbb{R}^{N}$. We give some information on the structure of those measures admitting as isoperimetric ...
Abstract: In this paper we start with the applications of polyfold theory to symplectic field theory.
Abstract: It is a well known fact that the union of the Reverse H\"{o}lder classes coincides with the union of the Muckenhoupt classes $A_p$, but the $A_\infty$ constant of the weight $w$, which is a ...
In this paper, we compute the Laplace transform of occupation times (of the negative half-line) of spectrally negative Lévy processes. Our results are extensions of known results for standard Brownia...
We consider nonlocal linear Schr¨odinger-type critical systems of the type 1/4v = v in IR. (1) where is antisymmetric potential in L2(IR, so(m)), v is a IRm valued map and v denotes the matrix mu...
For a domain D in Cz with smooth boundary and for a, b ∈ D, a 6= b, we have the circular (radial) slit mapping P(z)(Q(z)) on D such that P(z) − 1 z−a (Q(z) − 1 z−a ) is regular...
We observe that some special Itˆo diffusions are related to scattering properties of a Schr¨odinger operator on Rd, d  2. We introduce Feynman-Kac type formulae for these stochastic processes wh...
By proving an L2-gradient estimate for the corresponding Galerkin approximations,the log-Harnack inequality is established for the semigroup associated to a class of stochastic Burgers equations. As a...
We give a representation of the solution for a stochastic linear equation of the form Xt = Yt + R(0,t]Xs− dZs where Z is a c`adl`ag semimartingale and Y is a c`adl`ag adapted process with bounde...
We prove that every subgroup of p-power index in a right-angled Artin group is conjugacy p-separable. In particular, every right-angled Artin group is conjugacy p-separable. A consequence of this resu...
We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP...

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