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.

Quantum resonances describe metastable states created by phenomena such as tunnelling, radiation, or trapping of classical orbits. Mathematically they are elegantly defined as poles of meromorphically continued operators such as the resolvent or the scattering matrix: the real part of the pole gives the rest energy or frequency, and the imaginary part, the rate of decay. With that interpretation they appear in expansions of linear and non-linear waves. And they can be found in other branches of mathematics and science: as poles of Eisenstein series and zeta functions in geometric analysis, scattering poles in acoustical and electromagnetic scattering, Ruelle resonances in dynamical systems, and quasinormal modes in the theory of black holes. In my talk I will present some basic concepts and illustrate recent mathematical advances with numerical and experimental examples.