Pure Mathematics

The group of pure mathematics works with the theoretical problems arising in algebra, geometry and analysis, which have important applications in mathematical physics, relativity theory, quantum mechanics, coding theory and computer science, topology and number theory. Algebraic and differential equations are important tools of the research, which are carried on both abstract and computational levels. Lie theory, which focuses on various forms of the symmetry, is also part of the group activity.   The Group manages the Sophus Lie Seminar

Fields of research

Algebra

Analysis and Geometry

Algebraic geometry, codes and matroids

  • Producing error-correcting codes from algebraic varieties
  • Relationship between codes and matroids
  • Curves, surfaces and threefolds

Cohomology of quasi-groups

  • Homology and homotopy theory for general topological spaces

  • (Co)homology methods in cryptology 

Elliptic curves and number theory
  • Point counting on elliptic and hyperelliptic curves
  • Relationships between elliptic curves and ideal class groups in number fields and function fields
  • Diophantine and Analytic number theory

Differential geometry and Lie theory
  • Symmetry of geometric structures
  • Invariants of Lie groups and pseudogroups actions
  • Metric, conformal, projective, complex and contact geometry
Dynamical systems
  • Integrable Hamiltonian systems
  • Chaotic dynamics and topological entropy
Differential equations and Mathematical physics
  • Symmetries, differential invariants and equivalence
  • Solvability and integrability of ODEs and PDEs
  • Quantization theory and Relativity theory

 

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