Theoretical Physics and Cosmology

We investigate the possible nature of dark energy and dark matter from the viewpoint of diverse approaches to quantum gravity and modified gravity theory, as f(R), f(R,G) and certain non-local theories. Regularization procedures of quantum vacuum fluctuations by using techniques of operator zeta functions and other special functions of mathematical physics, as well as very useful formulas involving such functions, as several extensions of the celebrated Chowla-Selberg series formula, and their application in the calculation of determinants and effective actions in quantum field theory. Applications of the quantum vacuum fluctuations, the Casimir effect and other quantum effects to nanotechnology (MEMS and NEMS) and to fundamental aspects in cosmology. Uses of combinatorial and statistical methods in the study of the physics of dynamical systems .Analytical approaches to the Reimann conjecture.