The geometry of string theory and its implications for physics beyond the stand model

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One of the main challenges of theoretical physics is to provide a unified description of quantum physics and Einstein's theory of gravity. String theory is a promising candidate for such a theory. It has been studied extensively in the last decades, and has led to an impressive number of results, both in mathematics and physics. However, it is notoriously difficult to extract clear experimental predictions in the area of particle physics from string theory. One of the reasons being that the mathematics of string theory are very complicated, hence it is not easy to construct realistic string models which are simple enough mathematically. But very recently, a new class of string models has been discovered, with experimental signatures that could perhaps be observed at upcoming particle physics experiments, such as the Large Hadron Collider at CERN. These new models, which are called "F-theory compactifications", translate the physics of particles into a beautiful mathematical problem about the geometry of the internal space of the string compactification. My research program aims at studying this type of geometries in detail, with the explicit goal of extracting new results in particle physics from string models. From a different viewpoint, it turns out that by studying the same geometries we can also derive many new fascinating results in mathematics, which are consequences of the internal structure of string theory; this is the second facet of my research program.