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Morse Theory and Related Topics

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:

  1. J. Milnor, Morse theory. Princeton Univ. Press, 1963
  2. 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
Next Lectures: 

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