Lecturer:
Course Type:
PhD Course
Academic Year:
2019-2020
Period:
October - January
Duration:
60 h
Description:
The course includes:
- Classical Morse theory for smooth functions and regular variational problems.
- Morse theory for nonsmooth and, in particular, piecewise smooth functions.
- Symplectic interpretation of the Lagrange multipliers rule. Maslov index and its relation to the Morse index.
- Floer homology.
The only prerequisite beyond basic mathematical background is the elementary homology theory. No knowledge of symplectic or Riemannian geometry is expected.
I do not plan to follow any book. Standard sources are:
- J. Milnor, Morse theory. Princeton Univ. Press, 1963
- L. Nicolaescu, An invitation to Morse theory. Springer, 2011
Location:
TBC(to be checked)
Location:
A-138 on 18/02; A-134 on 25/02 and 28/02; A-136 otherwise