Research Themes
Six collaborative themes connecting pure mathematics with computational applications
Research themes
Current research themes across computational and pure mathematics.
As a collaborative initiative between the Universities of Tromsø and Bergen, the center serves as a national nucleus for mathematicians throughout Norway. We organize research into six interrelated themes addressing fundamental mathematical structures: CONnections, DEFormations, COMpositions, REPresentations, LINearization, and POLynomials.
These themes emphasize local-versus-global perspectives and algebraic bridges between continuous and discrete representations. With two core center members leading each theme, we coordinate joint work and collaboration across all research themes present at the LSC.
The themes reflect our basic philosophy: centering research around mathematical structures that are fundamental for a fertile interaction between computational and pure mathematics. The topics interlace and overlap in many ways, and we generously exchange ideas between different research themes and communities. We believe in the serendipity of science.
Our research addresses three fundamental questions: What are the underlying foundations of structured and efficient computations in mathematics? How does symmetry, respectively order, facilitate and structure computational processes? Which modern algebraic structures build new bridges between the continuous and the discrete?
Theme index
Theme pages include related projects and research context.
CONnections
RT1
Manifolds are the fundamental mathematical domains underlying differential equations and dynamical systems. Élie Cartan and Shiing-Shen Chern emphasized the importance of the notion of connections on manifolds, which provide geometric information, encode symmetries, and define parallel transport as a foundation of computational algorithms for deterministic and stochastic dynamical systems. Lie group integration techniques have emerged as a superior alternative to classical coordinate-based algorithms.
DEFormations
RT2
Deformation theory studies how mathematical structures can be continuously varied while preserving essential properties. This theme explores deformations of algebraic and geometric structures, with applications to moduli spaces, representation theory, and computational algebra.
COMpositions
RT3
Composition structures arise throughout mathematics, from the composition of functions to operads and higher algebraic structures. This theme investigates compositional patterns in algebra, topology, and their computational applications.
REPresentations
RT4
Representation theory provides powerful tools for understanding symmetry through linear algebra. This theme explores representations of groups, algebras, and categories, with applications to invariant theory and computational methods.
LINearization
RT5
Linearization techniques transform complex nonlinear problems into tractable linear ones. This theme studies linearization methods in differential equations, dynamical systems, and optimization, bridging continuous and discrete mathematics.
POLynomials
RT6
Polynomials form a bridge between algebra, geometry, and computation. This theme investigates polynomial systems, algebraic geometry, and their applications to optimization, coding theory, and computational complexity.