''... homines dum docent discunt." 




 Schedule of lectures:   Mondays  and  Wednesdays  from  10:00 - 11:30  in  Raum 313


 Exercise class: Monday 16:00 - 17:30 in Seminarraum 3. Find the weekly homework below


 Office Hours: Mondays 15:00 - 17:00 


 Teaching assistant: Dr. Thomas Rot  (contact:  thomas (dot) rot (at) uni-koeln (dot) de). Office hours: Thursdays 14:00 to 16:00.


 Language used in the lectures:  English


 Prerequisites:  Although some notions will be briefly recalled in class, it is recommended for the student to have a good background in Differential Geometry  and Algebraic Topology.





- “Lectures on Symplectic Geometry“ by Ana Cannas da Silva, Lecture Notes in Mathematics, Springer-Verlag. Available online here.

- "Introduction to Symplectic Topology" by Dusa McDuff and Dietmar Salamon, Oxford Mathematical Monographs.



 Introduction and some motivation...


Symplectic geometry was born about two centuries ago to provide the right mathematical framework for studying classical mechanics: the prototype of a symplectic manifold is the phase space of a particle moving in the three dimensional space. Since its origins, symplectic geometry has developed as an independent, fundamental branch of mathematics, having connections with complex geometry, algebraic geometry, mathematical physics and combinatorics. The aim of this course is to provide students with a general overview of basic concepts of symplectic geometry. We will closely follow the book ‘Lectures on Symplectic Geometry by Cannas da Silva, complementing some of the material with other sources. Time permitting, symplectic manifolds with group actions will be also treated. 


About the exam: It is going to be an oral exam. In order to be admitted, the average of the grades for the homework assignments must be greater or equal to 50/100. For the date, one possibility is July 21st, the other is September 15th. Later in September is also possible.
























   Symplectic Geometry


Prof. Dr. S. Sabatini

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


(Sommersemester 2015)


Info exam (click here)






The exercise sessions of Symplectic Geometry should be regarded as a fundamental, integral part of the course, aiming at making the comprehension of the subject much deeper and clearer. It is mandatory to register for the exercise sessions. The exercises will be available here below.



Homework 1 (Due on Monday April 20th 2015 in class)


Homework 2 (Due on Monday April 27th 2015 in class)


Homework 3 (Due on Monday May 4th 2015 in class)


Homework 4 (Due on Monday May 11th 2015 in class)


Homework 5 (Due on Monday May 18th 2015 in class)


Homework 6 (Due on Monday June 1st 2015 in class)


Homework 7 (Due on Monday June 8th 2015 in class)


Homework 8 (Due on Monday June 15th 2015 in class)


Homework 9 (Due on Monday June 22nd 2015 in class)


Homework 10 (Due on Monday June 29th 2015 in class)


Homework 11 (Due on Monday July 6th 2015 in class)


Homework 12 (Due on Monday July 13th 2015 in class)








© 2014 by SILVIA SABATINI. This website was created using Wix.com