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The two cornerstones of theoretical physics are quantum theory and our theory of gravity, Einstein's theory of General Relativity.The essence of quantum mechanics is that particles sometimes behave like waves and vice-versa. Three of the four known forces are quantum mechanical in nature. These are the electromagnetic, the weak nuclear and the strong nuclear forces. Indeed these force are described by the Standard Model of particle physics. This is a quantum field theory, more precisely a quantum Yang-Mills theory, and it has now been tested to extraordinary precision in particle accelerators.The fourth force, gravity, on the other hand hand, is described by General Relativity. It says that the phenomenon of, say, an apple falling onto Isaac Newton's head, is a manifestation of the curvature of space-time. To get a flavour of this, imagine a big latex rubber sheet with a shot-put sitting in the middle stretching it down. If we now put a marble on the sheet, it will roll toward the shot-put as if it is being pulled by some force.General Relativity is also very accurate, having been tested in many different ways. One of the most interesting aspects of the theory is that it predicts the existence of black holes. In a black hole gravity is so strong, that is, the curvature of spacetime is so great, that even light cannot escape. We now think that all galaxies have a huge black sitting at their centre. General Relativity is also the basis for our theory of the origin of the universe, that everything began about 10 billion years ago in a very tiny compressed state and then exploded - the Big Bang .So, we have two beautiful theories, the Standard Model and General Relativity, and both are very accurate. But they are mathematically incompatible! How can this possibly be? The point is that the two theories are associated with very different scales: on small scales, for current particle physics, gravity is so weak that we can just forget about it. Similarly, General Relativity is applicable on very large scales when all other particle forces are negligible. This is why we can have the two incompatible theories happily co-existing.However, we know that there are some situations where we need both theories: for example inside black holes and at the Big Bang. A theory that unifies the two is called a theory of quantum gravity. I work on a candidate quantum gravity called string theory. The main idea of string theory is that everything is really made up of very tiny little loops or segments of string. The oscillations of these strings, like the different notes on a violin, would each become, via quantum mechanics, a different elementary particle. If the string oscillates one way it's an electron, if it oscillates another way it's a proton and so on. Understanding the mathematics of exactly how this might happen is something that I work on. Interestingly, string theory is associated with very interesting mathematics, particularly geometry, and the interplay between the two is a great inspiration in my work.Symmetry has been a major guiding principle in constructing both the Standard Model and General Relativity. Now, every particle that we know of is either a boson or a fermion. The bosons, a photon for example, are associated with forces, while the fermions, an electron for example, are associated with matter. A very interesting symmetry, called supersymmetry, is essentially the only way to connect bosons with fermions via a symmetry. It is a central component of string theory and, based on a lot of hints, I think obtaining a deeper mathematical understanding of supersymmetry in string theory will lead to a deeper understanding of string theory itself. This is what I am proposing to work on and I hope that it will provide a significant step on the journey to determine whether or not Nature is described by string theory.
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