Some of my planned research projects include:  Jointly with Shelly Goldstein and others, analysis of cosmological scenarios in which every conceivable history passes through some low-entropy state at some time.  How can the known quantum theories without observers (Bohmian mechanics, "GRW" theory of spontaneous wave function collapse, many-worlds) be transferred to curved space-time?  Towards a precise formulation (and, if possible, derivation) of the second law of thermodynamics in the framework of quantum mechanics, analogous to Boltzmann's work in the framework of classical mechanics.   Time evolution of quantum wave functions near space-time singularities. When gluing two space-time manifolds together at their singularities, does the Schrodinger-Dirac time evolution extend mathematically across the singular surface? Can one "survive a space-time singularity"?

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