Teaching
I teach courses through which students acquire knowledge of the foundations of modern geometry. If these courses are arranged in the order in which I would recommend taking them (from top to bottom), the sequence is as follows:
Analytical Geometry (Part I)
LTMS.00.050 · 3 ECTS
Vectors, vector algebra, coordinate systems, equations of lines and planes.
Analytical Geometry (Part II)
LTMS.00.051 · 3 ECTS
Conic sections: ellipse, hyperbola, parabola. Quadric surfaces: ellipsoid, hyperboloids, paraboloids.
Differential Geometry
MTMM.00.060 · 6 ECTS
Theory of curves and surfaces.
Riemannian Geometry
LTMS.00.097 · 6 ECTS
Riemannian metric, Riemannian manifolds, Riemannian connection and its curvature, geometric foundations of general relativity.
Global Analysis
MTMM.00.047 · 6 ECTS
Smooth manifolds, connections, differential forms, integration on manifolds, Stokes' theorem, Maxwell's equations.
Seminar on Geometry and Topology
Students may also register for and participate in the research seminar "Seminar on Geometry and Topology". In this seminar, we consider research topics in modern geometry that go beyond the standard university curriculum.
Students are offered a selection of research topics. After choosing a topic, a student prepares a presentation and gives it at one of the seminar meetings. If the topic inspires the student to pursue further research, it may develop into a bachelor's thesis and, in the future, a master's thesis.