Almost Complex Geometry Seminar

Department of Mathematics
The Graduate Center of CUNY

Wednesdays 11:45am - 1:45pm
Room 6417
Organizers: Luis Fernandez, Scott Wilson Qian Chen

Scope: this seminar is devoted to all topics related to almost complex manifolds, including but not limited to: complex manifolds, symplectic topology and geometry, (almost) Kahler geometry, as well the tools of algebraic topology and geometric analysis that have proven useful in studying such structures. The goal is expose students and faculty to foundational material and present day research in a relaxed format that includes traditional lectures with an actively engaged audience.

Jump to present semester.

Fall 2017:

8/30: Scott Wilson
Organizational and introductory material

I will give introductory material on almost complex manifolds.

9/6: Scott Wilson
Differential operators on almost complex manifolds

This is a continuation of the previous talk.

9/13: Scott Wilson
Integrability of almost complex structures

I will describe several notions of integrability and show they are equivalent.

9/20: no meeting due to holiday

9/27: Scott Wilson
The exterior derivative on almost complex manifolds

10/4: Luis Fernandez
Metrics on almost complex manifolds (1)

10/11: Luis Fernandez
Metrics on almost complex manifolds (2)

I will describe the integrability condition in terms of torsion and the Levi-Cevita connection.

10/18: Scott Wilson
The Frolicher-Nijenhuis bracket

10/25: Qian Chen
Real Analytic integrable almost complex structures

I will prove the Newlander-Nirenburg theorem in the real analytic case.

11/1: Qian Chen
Real Analytic integrable almost complex structures

This is a continuation of last week's talk.

11/8: Matthew Cushman
Symplectic Reduction

This is an introduction to the subject, in preparation for next week's speaker.

11/15: Richard Cushman
The Twisting Tennis Racket

Abstract: This talk gives a mathematical explanation of the twisting phenomenon exhibited in the following experiment. Take a tennis racket and mark its faces so that they can be distinguished. Call one rough and the other smooth. Hold the racket horizontally so that the amoorh face is up. Toss the racket attempting to make it rotate about the intermediate principal axis, which is through the face and perpendicular to the handle. After one rotation catch the racket by its handle. The rough face will almost always be up! Thus the racket has made a near half twist around its handle.

11/22: No meeting this week.

11/29: Bora Ferlengez
The space of almost complex structures on S^6

I will describe a rational model of the space of almost complex structures on S^6.

Almost Complex Geometry Seminar

Department of Mathematics The Graduate Center of CUNY

Wednesdays 11:45am - 1:45pm Room 6417 Organizers: Luis Fernandez, Scott Wilson Qian Chen

Fall 2017:

8/30: Scott Wilson Organizational and introductory material

9/6: Scott Wilson Differential operators on almost complex manifolds

9/13: Scott Wilson Integrability of almost complex structures

9/20: no meeting due to holiday

9/27: Scott Wilson The exterior derivative on almost complex manifolds

10/4: Luis Fernandez Metrics on almost complex manifolds (1)

10/11: Luis Fernandez Metrics on almost complex manifolds (2)

10/18: Scott Wilson The Frolicher-Nijenhuis bracket

10/25: Qian Chen Real Analytic integrable almost complex structures

11/1: Qian Chen Real Analytic integrable almost complex structures

11/8: Matthew Cushman Symplectic Reduction

11/15: Richard Cushman The Twisting Tennis Racket