Minicourse Part 1: Chaofeng Zhu (Chern Institute/Nankai U)
Speaker: Chaofeng Zhu (Chern Institute/Nankai U; vis. prof. Roskilde University (DSE/IMFUFA))
Part of a lecture series/mini-course on multiplicity of geodesics via symplectic homology.
Fri July 18th: (Page for Part 1)
10-11 Coffee/tea (4th floor common room)
11-13 Lecture 1: Iteration theory of Maslov type index for symplectic paths (Room: 04.4.01)
13-15 Lunch + coffee/tea (4th floor common room)
15-17 Lecture 2: Common index jump theorem (Room: 04.4.01)
Tue August 12th: (Page for Part 2)
10-11 Coffee/tea (4th floor common room)
11-13 Lecture 3: Symplectic homology and contact homology (Room: 04.4.01)
13-15 Lunch + coffee/tea (4th floor common room)
15-17 Lecture 4: Multiplicity of closed characteristics (Room: 04.4.01)
Abstracts for the lectures: (All are held in Room 04.4.01 at MATH, U Copenhagen)
Lecture 1: Iteration theory of Maslov type index for symplectic paths (based on the work of Long's school)
Abstract: In this lecture, we will give the theory of Maslov index in the finite-dimensional case.
Based on the theory, we give the iteration theory of Maslov type index for symplectic paths developed in Long's school.
Based on the theory, we give the iteration theory of Maslov type index for symplectic paths developed in Long's school.
Lecture 2: Common index jump theorem (based on the work of Long's school)
Abstract: In this lecture, we will prove the common index jump theorem, which is one of the keys for Lectue 4.
Lecture 3: Symplectic homology and contact homology
Abstract: In this lecture, we give the definition of Symplectic homology and contact homology and gather the needed results for the proofs in Lecture 4.
Lecure 4: Multiplicity of closed characteristics
Abstract: In this lecture, we will report a recent result of V. Ginzburg and his coauthors: On a dynamically convex hypersurfaces of R2n, there exist at least n closed characteristics.
