Department of Mathematics
The Department of Mathematics of the University of Ioannina is the second oldest department at the University. Founded in 1966 in the city of Ioannina, it comprises - along with the Department of Physics and the Department of Chemistry - the School of Sciences. The Department is housed on the northwest side of the academic campus, in the Department of Mathematics Building.
In its 50-year existence, the Department has undergone several stages of development and growth. Today it plays an important role in the continued scientific progress of Ioannina, the region of Epirus and the country. The Department’s research work and presence are internationally recognized. The curriculum, both undergraduate and postgraduate, is characterized by pluralism while concurrently covering all modern disciplines of mathematical science. The Department of Mathematics strives to excel in the scientific training of its students and the honing of their abilities, in order to enable them to build the profile of the mathematician they desire to be.
We wish you a pleasant navigation experience and we are at your disposal in order to provide you with any further information regarding our Department.
ΓΕ8 - Special Topics in Geometry
Syllabus
- Bochner’s technique in Differential Geometry.
- Complex manifolds, Kähler manifolds, Riemann surfaces.
- Isometric and conformal immersions.
- Rigidity aspects of isometric immersions.
- Minimal submanifolds in Riemannian manifolds.
- Harmonic maps, geometric PDE’s and flows.
ΓΕ1 - Differential Geometry
Syllabus
- Manifolds of the Euclidean space.
- Tangent and normal bundles.
- 1st and 2nd fundamental forms.
- Weingarten operator and Gauss map.
- Convex hypersurfaces.
- Hadamard’s Theorem.
- 1st and 2nd variation of area.
- Minimal submanifolds.
- Weierstrass representation.
- Bernstein’s Τheorem.
ΓΕ3 - Riemannian Geometry
Syllabus
- Riemannian metrics, isometries, conformal maps.
- Geodesics and exponential maps.
- Parallel transport and holonomy.
- Hopf-Rinow’s Theorem.
- Curvature operator, Ricci curvature, scalar curvature.
- Riemannian submanifolds.
- Gauss-Codazzi-Ricci equations.
- 1st and 2nd variation of length.
- Jacobi fields.
- Comparison theorems.
- Homeomorphic sphere theorem
ΓΕ2 - Differential Geometry
Syllabus
- Topological and smooth manifolds.
- Tangent and cotangent bundles.
- Vector fields and their flows.
- Submanifolds and Frobenius’ Theorem.
- Vector bundles.
- Connection and parallel transport.
- Differential forms.
- De Rham cohomology.
- Integration.
- Stokes’ Theorem.