# Almost Complex Geometry Seminar

## Department of MathematicsThe Graduate Center of CUNY

### Wednesdays 11:45am - 1:45pm Room 6417 Organizers: Luis Fernandez, Scott WilsonQian 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.

### 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.

#### 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.

#### 10/25: 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.

#### 11/29: 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.