On the geometry of string theory and particle physics

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Geometry is omnipresent in modern physics, particularly in string theory. On the one hand, if string theory is to describe Nature, one must be able to extract observable physics from it. Most of the actual phenomenological studies of string theory have been done by studying the geometry of what is known as string compactifications. On the other hand, from a mathematical standpoint, string theory has proved amazingly effective at producing new conjectures and theorems, by exploiting the crucial physical idea of string dualities. Many of these new results relate geometry to other areas of mathematics, such as topology and number theory. My research project focuses on the fascinating interface between geometry and string theory. I plan on investigating striking new results in mathematics that stem from a novel recursive structure discovered in a particular string duality known as mirror symmetry. I also plan on studying the geometry of heterotic compactifications and scattering amplitudes in gauge theories, in order to deepen our understanding of particle physics and string theory.