The Department of Mathematics and Statistics has up to three PhD position vacant from 01.01.2027 for applicants who wish to obtain the degree of Philosophiae Doctor (PhD). The position is affiliated to the Lie-Størmer Center. The Lie-Størmer Center is jointly hosted by UiT The Arctic University of Norway (UiT) and University of Bergen (UiB), Norway. The center will employ up to 8 PhD Research Fellows, whose research will focus on the interaction between algebra, differential geometry, analysis and computational mathematics, as well as their applications to data science and computational dynamics. You can read more about the project on its homepage http://www.lie-stoermer.no. The project is funded by the Tromsø Research Foundation (TFS), UiT and UiB.

In this call, we are interested in hiring up to 3 candidates who will be employed at the Faculty of Science and Technology, UiT in Tromsø. The appointment is for a period of three to four years, depending on whether teaching duties will be assigned.
The nominal length of the PhD programme is three years. If a fourth year is assigned, it will be distributed as 25 % each year to teaching and other duties.

The objective of the position is to complete research training to the level of a doctoral degree. Admission to the PhD programme is a prerequisite for employment, and the programme period starts on commencement of the position.

The workplace is at UiT in Tromsø. You must be able to start in the position within six months after receiving the offer.

Research at the Lie-Størmer Center (LSC) aims to explore uncharted territory at the interface of computational and pure mathematics, targeting foundational mathematical challenges relevant to the modern information society and geometric dynamical control in engineering. This project builds bridges between pure and computational mathematics, among
Mathematics departments in Tromsø, Bergen, and across Norway, and between high-level research and education within the ERCOM network of European mathematical research centers.

Computational mathematics is a cornerstone of modern science. Its methods are reshaping the foundations of pure mathematics, while abstract mathematical concepts generate fresh insights into algorithms and discretization techniques – critical for numerical computations and simulations. This convergence signifies a pivotal phase in the mathematical sciences, where the divide between pure and applied mathematics is narrowing. Advancing this integration demands collaboration across these fields, which the Lie-Størmer Center will champion.

The project is organized in multiple thematic areas and interaction between them. The candidate should specify 1 or 2 areas that they are interested in and qualified for. If a candidate has the ability to contribute to more than one work package, this is counted as a positive.

•  Area1 - Lie Theory: Analysis and Geometry of Nonholonomic Systems
  ○ Areas of Research: Sub-Riemannian geometry and Cartan geometry, Vector Distributions and Supergeometry
  ○ Considered a plus: research/course focus on differential geometry. Knowledge of Lie theory, sub-Riemannian geometry or Cartan geometry, as well as proficiency in symbolic packages will count as a strong positive.
   
• Area2 – Polynomials, Ideals and Algebra
  ○ Areas of Research: Monomial and polynomial ideals, toric varieties, tropical varieties, relations to combinatorics.
  ○ Considered a plus: research/course focus on algebra or algebraic geometry.
   
• Area3 – Magnus Expansions and Signatures in Data Science and Engineering
  ○ Areas of Research: Signatures (in the sense of rough paths) applied to curves and surfaces, Magnus expansion, Hopf algebras, applications.
  ○ Considered a plus: research/course focus on stochastic analysis, algebra or rough paths. Knowledge of Lie theory or Hopf algebra will be considered as a benefit.
   
• Area4 - Algebra, Geometry and Topology for Complex Data Analysis
  ○ Areas of Research: Algebraic methods in data analysis, optimization, topological data analysis, geometric deep learning.
  ○ Considered a plus: experience in programming or course work in computer science, algebra, real algebraic geometry, topology or differential geometry, topological data analysis or machine learning.