Back to Mark McLean's Homepage

MAT 620 Topics in Topology: Introduction to Symplectic Geometry

Course Instructor: Mark McLean

Tuesday and Thursday 2:30pm- 3:50pm in Physics P122.

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.

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 1pm-2pm (advising), Tuesday 1pm-2pm and Wednesday 11am-12pm (4-114)

Student Accessibility Support Center (SASC) Statement:
If you have a physical, psychological, medical or learning disability that may impact your course work, please contact the Student Accessibility Support Center (SASC), ECC (Educational Communications Center) Building, room 128, (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 the staff at the Student Accessibility Support Center (SASC). 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.