My own research in mathematical cosmology is concerned with developing new geometric extensions of general relativity and studying cosmological problems by employing global geometric, dynamical, and topological methods. Some highlighted keywords for my research over the years have been: Synchronization in cosmology, chaotic Mixmaster oscillations, conformal methods in cosmology, ambient cosmological metric, no-scale gravity, singularities, completeness, inflation, multiverse, cosmological constant, higher-order gravity, scalar-tensor theory, stability in cosmology.