his talk will be about the interplay between polynomials
whose zero sets interact with the n-torus in C^n (in several natural
ways) and operator related complex function theory (in several natural
settings). Interpolation problems for analytic functions, sums of
(Hermitian) squares formulas, and reproducing kernels all play
important roles. The talk will be relatively non-technical.

This talk will be about a general framework of image processing such as Image denoising, deblurring, segmentation, etc. Variational and also PDE approaches will be considered. Various function spaces will also be mentioned and we will see some advantages and disadvantages of the functions spaces. At the end,
noise - texture characterization or separation techniques will be discussed. Notice that there are no mathematical definitions of noise and texture yet. We will think about this too.

Professor Fred Wan will describe some highlight of his 50 years long journey in applied mathematics research at four institutions. He will touch on scientific topics such as mechanics, economics, and the biology of Morphogens that guide tissue development.

In this talk, we consider the family of pseudo differential operators $\{\Delta+ b \Delta^{\alpha/2}; b\in [0, 1]\}$ that evolves continuously from $\Delta$ to $\Delta + \Delta^{\alpha/2}$. We establish a uniform boundary Harnack principle with explicit boundary decay rate for nonnegative functions which are harmonic with respect to $\Delta +b = \Delta^{\alpha/2}$ (or equivalently, the sum of a Brownian motion and an independent symmetric $\alpha$-stable process with constant multiple $b^{1/\alpha}$) in $C^{1, 1}$ open sets.