Subject of the project
In mathematics, many families of complex manifolds are parametrized by so-called Shimura varieties. These are highly symmetric objects related to very different parts of mathematics (including representation theory, number theory, differential geometry). Thanks to these connections, they have been studied extensively in the past 40 years, and we know have a rich understanding of complex manifolds that are parametrized by Shimura varieties.
However, most families of complex manifolds are not parametrized by Shimura varieties. This includes for example the Calabi-Yau threefolds ocurring in certain models of string theory. In this project we will move beyond the comfort zone of Shimura varieties and start studying geometric and arithmetic aspects of families of complex manifolds that are not parametrized by Shimura varieties.