Educational Sciences and Mathematics
Algebra and Analysis with Applications
The research group conducts research in algebra, analysis, geometry, and their applications.
Research directions
Algebraic Combinatorics
We study algebraic combinatorics. Our research includes matroids, polymatroids, and their generalizations, with applications in algebra and information theory.
Faculty members: Lisa Nicklasson
External link. and Thomas Westerbäck External link.
Algebraic Geometry and Commutative Algebra
We study algebraic geometry and commutative algebra. Our research includes cohomology of moduli spaces and computational, combinatorial, and homological aspects of commutative algebra and its applications.
Faculty members: Olof Bergvall External link., Lisa Nicklasson External link., and Peder Thompson External link.
PhD students: Emily Berghofer External link. and Tianqi Liu External link.
Nonassociative Algebra and Noncommutative Algebra
We study nonassociative and noncommutative algebra. Our research includes graded and filtered noncommutative rings, their nonassociative generalizations, and hom-algebraic structures, such as hom-associative and hom-Lie algebras.
Faculty members: Masood Aryapoor External link., Per Bäck External link., Lars Hellström External link., and Sergei Silvestrov External link.
PhD students: Mudassar Ahmad External link. and Germán García External link.
Noncommutative Analysis and Noncommutative Geometry
We study the interplay between operator algebras, dynamical systems, and iterated function systems. Our research focuses on noncommutative operator algebras and operator systems, including noncommutative families of bounded and unbounded operators on Hilbert and Banach spaces. This work spans C*-algebras, von Neumann algebras, Banach and normed algebras, exploring their fundamental role and significant applications in noncommutative analysis, noncommutative geometry, quantum physics, quantum computing, and quantum information theory.
Faculty members: Sergei Silvestrov External link.
Operator Theory and Harmonic Analysis
We study spaces of analytic functions and related operators. Particular interest is devoted to approximation problems motivated by questions in harmonic analysis, operator theory and applications.
Faculty members: Bartosz Malman External link.
Contact
Ongoing research projects
The project concerns questions in Fourier analysis related to spectral structure of functions with various unilateral decay conditions. The research is motivated by applications in theory of linear operators and other parts of mathematics.
Project manager at MDU: Bartosz Malman
Main financing: Vetenskapsrådet