Back to Mark McLean's Homepage

MAT 562: Symplectic Geometry

Course Instructor: Mark McLean.

Monday and Wednesday 11:30am-12:50pm, Physics P123.

Introduction to the Course

This course is an introduction to Symplectic Geometry. We will be studying symplectic manifolds, which can be thought of as spaces in which one can naturally write down using Hamiltons equations. We will introduce many of the key objects in this field such as Lagrangian, isotropic, coisotropic submanifolds. We will also give an introduction to moment map theory and toric geometry. We will also cover the ideas behind Gromov's non-squeezing theorem.

McDuff, Dusa, and Dietmar Salamon. Introduction to symplectic topology. Vol. 27. Oxford University Press, 2017.

Ana Cannas Da Silva. Lectures on symplectic geometry. Vol. 1764. Springer Science & Business Media, 2001.


You should be very familiar with topics in Differential geometry such as Sards Theorem, Implicit Function theorem, connections and curvature etc.

Office Hours: Monday and Wednesday 10am-11am (3-112).


Homework 1 (Due Sep 14)
Homework 2 (Due Oct 05)
Homework 3 (Due Oct 19)
Homework 4 (Due Nov 9)
Homework 5 (Due Nov 30)

Disability Support Services (DSS) Statement: If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, (631) 632-6748, or at They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: and search Fire Safety and Evacuation and Disabilities.

Academic Integrity Statement: Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the academic judiciary website at

Critical Incident Management Statement: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Student Conduct and Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Schedule, and the Faculty-Employee Handbook.