Geometrical physics is a unified approach to all fundamental theoretical physics. The basic structures of classical mechanics, electrodynamics, relativity, thermodynamics, and gauge theory are geometric in nature, and I am interested in unified geometrical approaches to each one of these branches of theoretical physics.
Mathematical cosmology is defined, informally speaking, as the study of whole universes. It started in 1917, when Albert Einstein showed how to build the first universe as a solution of his equations of general relativity. Since then, it has developed into a vast theoretical science that aims to study `universes’, solutions of Einstein’s and other gravity theories, and confront with the latest observations.
Mathematical cosmology uses geometrical physics methods to study implications for the possible universes. It has freed us from prejudices about our Universe, by separating the always unknown and unknowable Universe, from the many different universes-the possible constructions of mathematical and physical models of the Universe that we can build, study, and compare!