Time evolution in string theory

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Einstein's theory of general relativity describes gravitational forces between large objects, forces such as the attraction between the Earth and the Sun, those holding the Milky Way galaxy together and those forces determining the rate of expansion of the Universe since the Big Bang. It is an accurate theory and its predictions have been tested in experiment and observation. Quantum Mechanics is the theory of the small: the atom, as well as the atom's constituents.  It governs the behaviour of semiconductors, of chemical reactions and of elementary particles, from the every-day electrons to the exotic top quark.  The theory agrees with experiments with an unprecedented accuracy. These two theories seem to have little in common; however, the study of some objects and phenomena requires us to use of both of them.  This includes attempts to understand the interior of a black hole, such as the one believed to exists at the center of our Galaxy.  Another example is the split-second after the Big Bang, when our just-born Universe was incredibly small, dense and hot.  String theory is our best candidate for a framework in which these two theories can be brought together.  In the last three decades, string theory has made great advances in our understanding of the interplay between Gravity and Quantum Mechanics.  Experiment and observations continue to challenge the theory; the most recent such challenge, issued by Cosmology through the measurement of a positive cosmological constant, has yet to be answered. In my work, I focus on those problems I believe are going to be essential in answering this challenge: the methods for addressing time evolution in String theory.  The implications of my work range from the problems of evolution of the Universe as a whole to the questions of how black holes decay.