M-branes, noncommutative geometry and thermodynamics of charged rotating (A)dS spacetimes with a NUT twist

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One of the most interesting and attractive problems in physics is that of understanding how to make sense of a quantum theory of gravity. My long-term research involves strengthening and increasing our knowledge of particle and gravitational physics by considering specific questions connected with quantum gravity from the viewpoints of particle physics, noncommutative geometry and gravitational physics. According to our present knowledge, the best possible candidate theory for a quantum theory of gravity is superstring theory, which seems to exhibit good perturbative behaviours. In superstring theory, all the fundamental particles in particle physics and all known forces in nature are realizations of different states of the most fundamental object that is a one-dimensional string. However it has been known for some time that there are at least five distinct consistent superstring theories. It seemed that they simply exist with some dual relations between them although there was no known theory that explained why different superstring theories could have dual relations between them. In this regard, it was very difficult to determine which particular string theory describes our real world. Recent developments in non-perturbative string theory -- starting with the discovery of various extended objects in superstring theories (Dirichlet branes) -- have begun to cast light on this important question. It has become clear that these extended objects play very important roles in the strong dynamics of superstrings and in Membrane theory (M-theory). Superstring theories, when viewed in the strong coupling limit, are not just theories of strings but instead contain many extended objects (branes) as light degrees of freedom. The existence of these objects turned out to be the origin of the dual relations between different superstring theories. M-theory as it is called at present, is an eleven dimensional quantum theory of the many extended objects which produce all the superstring theories around its perturbative vacua. In this context my research plan will address current issues in particle physics, noncommutative geometry and gravitational physics that are inspired by string theory.