The Department of Mathematics and Mathematical Statistics is offering a postdoctoral scholarship within the project “Computing representation theory using statistical mechanics”. The scholarship is full-time for two years starting preferably in January 2025 or by agreement.

The project is led by Henrik Gustafsson in a newly formed research team in representation theory and number theory at Umeå University. Together with his PhD student Gustafsson is working in p-adic representation theory and, more specifically, on combinatorial descriptions of p-adic Whittaker functions in terms of partition functions of solvable vertex models from statistical mechanics.

The team is also part of the research group in group theory and the broader research domain discrete mathematics with a rich history at the department covering a wide range of areas: extremal, probabilistic, algorithmic, game theoretic, computational, topological, geometric and algebraic aspects of combinatorics.

The postdoctoral scholarship is dedicated to the scholar’s own professional and intellectual development and does not include any teaching duties.

Project description
Whittaker functions are used to describe and characterize p-adic representations and they appear as local constituents of automorphic forms which are central objects in number theory.

The project concerns a combinatorial description of the values of such Whittaker functions using six-vertex lattice models. These lattice models are described by weighted paths through a square lattice and satisfy strong solvability conditions related to quantum groups. Using the properties of these vertex models one can then discover and prove identities for the original Whittaker functions in representation theory.

Recently, Gustafsson and his international co-authors discovered a surprising duality between two different kinds of Whittaker functions in the paper https://doi.org/10.1112/jlms.12896. These Whittaker functions describe two very different generalizations: a representation theoretical, Iwahori, refinement, and a number theoretical, metaplectic, generalization and are, at a first glance, not expected to be related. Their lattice model descriptions are however very similar, and in this perspective the duality becomes a natural, but non-trivial, equality of partition functions.

The aim of the research project is to explain the quantum group foundations of this equality of partition functions towards the long-term goal of understanding the underlying representation theoretical mechanisms for the duality.

The postdoctoral scholarship is financed and administered by The Kempe Foundation (JCSMK24-0117). The stipend will be 737 000 SEK for two years, meaning 368 500 SEK per year.

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://www.umu.se/en/work-with-us/postdoctoral-scholarships/6-1236-24/