This grant will enable him to hire a PhD-candidate who will work on the the Langlands programme with him. This program aims to establish connections between very different parts of mathematics, so that problems in one field can be transferred to another field, where they could become more manageable. In this project, a particular link between number theory and analysis will be investigated.
An important property of a representation is the dimension of the underlying vector space - that is, if it has finite dimension. If a representation has infinite dimension, there is a preferable, analytic substitute for the dimension, known as the formal degree.
The driving conjecture of this project asserts that these formal degrees are equal to certain purely arithmetic expressions. A proof of this formal degree conjecture would fill a hole in the local Langlands programme and would mean progress in both representation theory, analysis and number theory.