Research
The Chair of Mathematics makes research in various areas of pure and applied mathematics. One of the main focuses of research is related to generalisations of the complex analysis to higher dimensions. In particular, quaternionic and Clifford analysis are among the main topics of research. The Chair of Mathematics makes research in active cooperation with colleagues from different countries: Belgium, Czech Republic, Finnland, France, Germany, Israel, Italy, Mexico, Portugal, Russia, Turkey, UK, Ukraine, USA.
The Chair of Mathematics also host the web-site of the International Conference Series on Clifford Algebras and Their Applications in Mathematical Physics: https://projekte.uni-erfurt.de/icca/
The following topics are of particular interest at the chair:
- Dirac and Laplace operator on manifolds
- Complex and hypercomplex analysis
- Clifford analysis
- Harmonic and hypercomplex automorphic forms
- Analysis of partial differential equations
- Fractional differential and integral calculus
- Special functions
- Slice-monogenic functions
- Octonions
- Superoscillations
- Non-commuative geometry
- Non-abelian gauge theories
- Numerical analysis
- Mathematical modelling
- Applied category theory
- Functional programming
- Dicsrete function theory
- Discrete Clifford analysis
- Exterior calculus
