Algebra and Analysis with Applications

Algebraic Combinatorics

We study algebraic combinatorics. Our research includes matroids, polymatroids, and their generalizations, with applications in algebra and information theory.

Faculty: Lisa Nicklasson External link. and Thomas Westerbäck External link.

Commutative Algebra and Algebraic Geometry

We study commutative algebra and algebraic geometry. Our research includes computational, combinatorial, and homological aspects of commutative algebra and its applications.

Faculty: 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: 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.

Faculty: 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: Bartosz Malman External link.