Postdoctoral scholarship (2 years) within Representation theory and Number theory
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.
Qualifications
To qualify as a postdoctoral scholarship holder, the postdoctoral fellow is required to have completed a doctoral degree or a foreign degree deemed equivalent to a doctoral degree. This qualification requirements must be fulfilled no later than at the time of the decision about scholarship recipient.
Priority should be given to candidates who completed their doctoral degree, according to what is stipulated in the paragraph above, no later than three years prior. If there are special reasons, candidates who completed their doctoral degree prior to that may also be eligible. Special reasons include absence due to illness, parental leave, appointments of trust in trade union organizations, military service, or similar circumstances, as well as clinical practice or other forms of appointment/assignment relevant to the subject area.
The doctoral degree should be in mathematics or be deemed to provide equivalent academic competence.
A successful candidate is expected to have a background and experience in one or several of the following subjects: (p-adic) representation theory, solvable lattice models, quantum groups, or number theory or related subject. It is advantageous to have previous publications within any of the listed areas, and particularly the first three.
Fluency in the English language, both written and spoken, is required. Good communication and collaboration skills are highly desirable.
Application
A full application should include:
Cover letter in which you shortly describe your research experience and planned future research as well as how these fit with the research described in this advertisement (maximum of 2 pages),
Curriculum vitae (CV) with a complete list of publications,
A separate list of your (up to) three most relevant publications. Briefly describe your own contributions to these publications and the relevance of the publications with respect to this advertisement (at most a total of one page). Please provide DOI links or similar for the three publications, and if they are not available as Open Access, then please include PDF copies of the publications with your application.
Verified copy of doctoral degree certificate or documentation that clarifies when the degree of doctor is expected to be obtained,
Verified copies of other diplomas, list of completed academic courses and grades,
Copy of your doctoral thesis (or draft of thesis if not yet completed),
Contact information to two persons willing to act as references. Please describe how these references are professionally related to you.
Other documents that the applicant wishes to claim.
The application should be written in English or Swedish. Your complete application, marked with reference number FS 2.1.6-1236-24, should be sent electronically (in PDF format) to medel@diarie.umu.se (with reference number on the subject line). The closing date for applications is September 16, 2024.
Umeå University strives to offer an equal environment where open dialogue between people with different backgrounds and perspectives lay the foundation for learning, creativity and development. We welcome people with different backgrounds and experiences to apply for this scholarship. The Department of Mathematics and Mathematical Statistics values the qualities that gender balance brings to the department, and therefore, we particularly encourage female and non-binary applicants.
More information
For more information, please contact assistant professor Henrik Gustafsson: henrik.gustafsson@umu.se.
