discipline

 MSC in Mathematics, Pure Mathematics, Elective Course

subject

 General Structures in Differential Geometry

lecturers

 Dr. Balázs Csikós (associate professor)

 Dr. Gyula Lakos (assistant)

 Dr. Gábor Moussong (assistant professor)

 Dr. László Verhóczki (associate professor)

credits

 2

period

 4th semester

curriculum

Optional topics:

Hyperbolic manifolds. The Mostow rigidity theorem. Hyperbolic geometry in the theory of 3-dimensional manifolds. Elements of the Thurston-Jorgensen theory.

Symplectic manifolds. Darboux theorem. Poisson manifolds. Symplectic structure on the orbits of co-adjoint representations. Geometric quantization of symplectic manifolds. The orbit method.

Distributions. Frobenius theorem. Lagrange functions, and Euler-Lagrange equation. Noether’s theorem. Legendre transformation. Connection between the Hamiltonian and Lagrange formalism.

Clifford and spin structures. Dirac operators. Index theorems. The heat equation method. Pseudodifferential operators. Ellipticity, Fredholm properties.

literature

 

form of tuition

Two hours of lecture per week.

mode of assessment

 oral exam