MAT 620 Tuesday, Wednesday Thursday 11:30am-12:50am, Mathematics 5127

MAT 620 Topics in Topology: Introduction to Symplectic Topology

Course Instructor: Mark McLean

Tuesday, Wednesday Thursday 11:30am-12:50am, Mathematics 5127

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. Finally, we'll explain some of the key ideas (without many proofs) behind Gromov's non-displaceability theorem. We will use the following books:

Dusa McDuff and Dietmar Salamon. Introduction to symplectic topology. Oxford University Press, 1998.

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

Prerequisites

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

Office Hours: Mon 2pm-3pm (Math learning center); Tu and Thur 10.30am-11:30am (4-101B)

Disability Support Services (DSS) Statement: If you have a physical, psychological, medical, or learning disability that may affect your course work, please contact the office of Disabled StudentServices (DSS), Educational Communications Center (ECC) Building, room 128, telephone (631) 632-6748. They will determine with you what accommodations, if any, 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 Disability Support Services. For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/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 are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website, http://www.stonybrook.edu/commcms/academic_integrity/index.html.

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 Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.