The Department of Mathematics and Mathematical Statistics is opening a PhD position in mathematics specialising in representation theory and number theory. The position covers four years of third-cycle studies, including participation in research and third-cycle courses. The last day to apply is 14 May 2023.

Project description and tasks:

The PhD student will carry out research in primarily representation theory, but also in number theory as part of a project supervised by Henrik Gustafsson. The main focus of the project is representations of p-adic groups where p is a prime number, and especially so-called Whittaker functions which describe these representations and frequently also appear in number theory.

Surprisingly, these functions can in several cases be computed by partition functions of exactly solvable models from statistical mechanics described by paths in a two-dimensional lattice. The fact that the lattice model is solvable means that the partition function satisfies a so-called Yang–Baxter equation related to a quantum group which we can use to derive identities for the original Whittaker function.

The aim of the project is to explain and expand on the web of unexpected and detailed connections that have been discovered between these very different objects with applications to number theory, combinatorics and statistical mechanics.

The research is part of a new initiative in the research field of representation theory by the department and a part of the existing research group in discrete mathematics which at the moment consists of 18 people of which 3 are PhD students. The department for mathematics and mathematical statistics as a whole has about 100 employees with about 20 PhD students. There are ample opportunities for international collaborations in the project.

Umeå offers excellent working and living conditions. The city is young and located right next to a large river. It is surrounded by forests and lakes and lies close by the sea. In the vicinity there are plenty of opportunities for both indoor and outdoor activities.

For further information and instructions on how to apply, see:

https://umu.varbi.com/en/what:job/jobID:616296/