Morse Theory seminar

Prof. Dr. S. Sabatini

(contact: sabatini (at) math (dot) uni-koeln (dot) de)

(Sommersemester 2015)

First meeting: Tuesday April 7th

Schedule of presentations: Tuesdays - 14:00 - 15:30 in Seminarraum 1 des Mathematischen Instituts (Raum 005)

Teaching assistant: Dr. Thomas Rot (email: thomas (dot) rot (at) uni-koeln (dot) de)

Language of the oral presentations: English

The Morse theory seminar is devoted to introducing master students in Mathematics to “Morse theory“ which, in loose terms, enables one to study the topology of the manifold from the critical points of special functions defined on the manifold, called ‘Morse function’. A good knowledge of Differential Geometry and Algebraic Topology is required.

Bibliography:

We will cover some of the material in the books:

- “Morse Theory“ by John Milnor (Annals of Mathematic Studies)

- “An Introduction to Morse Theory“ by Yukio Matsumoto (Mathematical Monographs).

Depending on the level of the students, topics from relevant articles may also be treated.

Seminars:

Tuesday April 7th: During the first meeting we will discuss about the material which will be presented during the semester. The first seminar talk will be on Tuesday April 14th.
April 14th: Alessandro Fasse "Morse theory on Surfaces"
April 21st: Philip Matura "Reeb Theorem"
April 28th: Isabelle Charton "Homotopy type in terms of critical values"
May 5th: Alessandro Fasse "Morse Inequalities"
May 12th: Martin Fechtner "Existence of non-degenerate functions" (Part I)
May 19th: Martin Fechtner "Existence of non-degenerate functions" (Part II)
June 2nd: Isabelle Charton "The Lefschetz Theorem"
June 16th: Philip Matura "The Levi-Civita connection"

"Young man, in mathematics you don't understand things. You just get used to them." - John von Neumann