University of Illinois at Urbana-Champaign

Math 520 - Symplectic Geometry - Fall 2019

(section A1)

Symplectic structures originated from the geometric formulation of classical mechanics. Nowadays, symplectic geometry is a central field in Mathematics with many connections with other fields, both in and outside Mathematics. This course presents an introduction to the foundational tools, ideas, examples and theorems of symplectic geometry. It is intended for PhD students studying symplectic geometry, Poisson geometry, and symplectic topology, as well as students in related areas such as dynamical systems, algebraic geometry, complex geometry, low dimensional topology and mathematical physics. The course covers the local and global structure of symplectic manifolds, their submanifolds, the special automorphisms they support (Hamiltonian flows), their natural boundaries (contact manifolds), their special geometric features (almost complex structures), and their symmetries. Students taking this course are assumed to know differential geometry at the level of Math 518 - Differentiable Manifolds.

Lecturer: Rui Loja Fernandes
Email: ruiloja (at)
Office: 346 Illini Hall
Office Hours: Mondays and Fridays 1.30-2.30 pm (or by appointment);
Class meets: MWF 9:00-9:50 AM, 447 Altgeld Hall;
Prerequisites: Math 518, or equivalent.

In this page:




Grading Policy

Homework Assignments, Lecture Notes and Sections covered so far:

All homework sets are from the book by Cannas da Silva:

Lecture Notes (Disclaimer: this contains mistakes! Better read the book...)

Sections of the book covered so far: 1.1-1.4; 2.1-2.4; 3.1-3.4; 4.1.-4.3; 5.1, 7.1-7.3, 8.1-8.3, 9.1-9.4, 10.1-10.3, 11.1-11.3, 12.1-12.3, 13.1-13.3, 14.1-14.3, 15.1-15.3, 16.1-16.4, 17.1-17.4, 18.1-18.4, 21.1-21.5, 22.1-22.4, 23.1-23.3.

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Last updated December 6, 2019.