Homotopy theory and quantum gravity

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My research involves topology, physics, computation, and various topics in between. Topology is the study of surfaces and higher-dimensional shapes, and the ways in which they can be stretched, deformed and mapped into each other.  A common technique is to study spaces by probing them with loops, spheres and other geometrically regular spaces.  This generally results in algebraic invariants. More recently, the ideas of topology are finding applications in other fields, such as algebra, algebraic geometry and physics.  There are many questions and techniques that make sense in all of these settings, and the main theme of my work in topology is the study of such global problems. This interplay between disciplines has proven to be extremely fruitful, and I will continue work in this direction. One of the most important unsolved problems in physics is the unification of general relativity, Einstein's highly successful theory of gravity, with quantum mechanics, which describes all the other known forces.  My work focuses on a promising approach to this problem, a theory called loop quantum gravity. Currently two of the biggest open problems in loop quantum gravity are the study of its classical limit and the ways in which matter can be introduced into the theory.  The classical limit problem asks what the large scale behaviour of the theory is, and compares it to known cosmological data. Introducing matter into the theory is important in order to learn what corrections the theory makes to the existing theory of particle physics, and to see if any of these predictions are experimentally testable. I will study these problems both analytically and through the use of computer simulations. Such work is an important test of a theory and can lead to improvements and other developments.