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.

I will discuss a basic result on the theory of chemical
reaction networks developed by Feinberg and others, which provides some
insight on the possible behaviors e.g. of protein networks inside a
cell. Then I will discuss an application of this theory to the study
of stochastic chemical reactions

I will start by giving a brief history of the subject and continue by presenting some important results in the field such as the "prime number theorem," and the mathematicians that contributed to these results. I will go on and give a very general discussion about the "Riemann Zeta Function," and discuss its importance in the field and mathematics in general. I will also touch upon some open problems such as the "Riemann Hypothesis," and "The Circle Problem." I will end my talk by discussing some recent and important results in the field such as the "Tao - Green" theorem on arithmetic progressions of prime numbers.

It is well-known that classical electrodynamics encounters serious
problems at microscopic scales. In the talk I describe a neoclassical
theory of electric charges which is applicable both at macroscopic and
microscopic scales. From a field Lagrangian we derive field equations,
in particular Maxwell equations for EM fields and field equations for
charge distributions. In the nonrelativistic case the charges field
equations are nonlinear Schrodinger equations coupled with EM field
equations. In a macroscopic limit we derive that centers of charge
distributions converge to trajectories of point charges described by
Newton's law of motion with Coulomb interaction and Lorentz forces. In a
microscopic regime a close interaction of two bound charges as in
hydrogen atom is modeled by a nonlinear eigenvalue problem. The critical
energy values of the problem converge to the well-known energy levels of
the linear Schrdinger operator when the free charge size is much larger
than the Bohr radius. The talk is based on a joint work with A. Figotin.