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

理论物理学的主要挑战之一是提供量子物理学和爱因斯坦引力理论的统一描述。弦理论是这种理论的一个很有希望的候选者。在过去的几十年里，人们对它进行了广泛的研究，并在数学和物理学方面取得了令人印象深刻的成果。然而，在粒子物理领域，从弦理论中提取明确的实验预测是出了名的困难。其中一个原因是弦理论的数学非常复杂，因此不容易建立足够简单的数学模型。但就在最近，一种新的弦模型被发现，其实验特征可能会在即将到来的粒子物理实验中被观察到，比如欧洲核子研究中心的大型强子对撞机。这些被称为“f理论紧化”的新模型，将粒子物理学转化为一个关于弦紧化内部空间几何的美丽数学问题。我的研究计划旨在详细研究这种几何形状，明确的目标是从弦模型中提取粒子物理的新结果。从不同的角度来看，通过研究相同的几何形状我们也可以在数学中得到许多新的迷人的结果，这些结果是弦理论内部结构的结果；这是我研究项目的第二个方面。

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.