Back to Mark McLean's Homepage

MAT 620:Topics in Topology: Stein Manifolds and Weinstein Manifolds

Course Instructor: Mark McLean

Tuesday, Thursday 11:30am-12:50pm, Mathematics 4130

Introduction to the Course

In this course we will explore the relationship between Stein geometry and symplectic geometry pointed out originally by Eliashberg and Gromov. A Stein manifold is a closed properly embedded complex submanifold of \C^N. One should think of this as the complex analytic analogue of a smooth affine variety. We will study certain natural deformation classes of these manifolds called Stein homotopy classes. In this course we will show that such a problem is equivalent to studying deformation classes of purely symplectic objects called Weinstein manifolds. We will also explain which almost complex manifolds are smoothly deformation equivalent to Stein manifolds. If there is time we will give examples of symplectically exotic Stein manifolds. We will be following the book From Stein to Weinstein and Back, Symplectic Geometry of Affine Complex Manifolds by Kai Cieliebak and Yakov Eliashberg. This is an advanced course.


You need to know some symplectic geometry and some complex geometry.

Office Hours: Tuesday 2pm-3pm (P143) Tuesday 3pm-4pm (Math 4-101B). Wednesday 11am-12pm (Math 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:

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,

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.