University of Illinois at Urbana-Champaign

Math 595 - Poisson Geometry - Spring 2020

(section FER)

This course is an introduction to Poisson geometry. Poisson geometry is the study of differentiable manifolds equipped with a Poisson bracket. Its roots lie in Classical Mechanics, but it became an independent field of study in the 70's and in the 80's, in parallel to its close cousin Symplectic geometry. If you have a basic knowledge of manifolds, vector fields and differential forms, you can get an idea of what Poisson geometry is by reading a brief introduction or looking at the following slides.

In this course I will be following a book that I am writting with Marius Crainic and Ioan Marcut. You can check the table of contents.

Students taking this course are assumed to know differential geometry at the level of Math 518 - Differentiable Manifolds.

Email: ruiloja (at)
Office: 346 Illini Hall
Office Hours: MF 1:30-2.30 pm (or by appointment);
Class meets: 9:00-9:50 AM MWF 441 Altgeld Hall
Prerequisites: Math 518 or equivalent.

In this page:




I will provide to participants some lecture notes as the course progresses, but the following two references should also be very helpful:

Grading Policy

On-line classes

Chapters 1-7 of the Lecture Notes were covered in the face-to-face lectures.

(PDF files can be viewed using Adobe Acrobat Reader which can be downloaded for free from Adobe Systems for all operating systems.)

Emergency information for students in Mathematics courses

For important emergency information related to fires, tornados or active threats, please look at the following leaflet.

Last updated April 20, 2020.