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.

Fall 2018:

date: 9/12
Organizational and introductory material

Welcome new students!

date: 9/19
No seminar or classes due to holiday

9/26: Scott Wilson
Title: Dolebault cohomology for almost complex manifolds

Abstract: I will report on recent work with Joana Cirici that extends the Dolbeault cohomology and its surrounding theory to the case of arbitrary almost complex manifolds. A spectral sequence will be described and explicit calcualtions will be done in the case of some interesting Lie groups and nilmanfiolds. I'll also describe some degeneration results and an application that shows this cohomology can be used to show certain almost complex manifolds do not admit nearly Kahler metrics.

10/3: Scott Wilson
Title: Dolebault cohomology for almost complex manifolds (part II)

Abstract: This will be a continuation of the previous talk. I'll do some hands on calculations and examples, and describe the harmonic theory that accompanies the Dolbeault theory. If time permits, I'll describe some degeneration results and applications to nearly Kahler 6-manifolds.

10/10: Luis Fernandez
Title: Introduction to Kahler manifolds

Abstract: I will describe foundational material concerning Kahler manifolds.

10/17: Aleksander Doan (Stony Brook University)
Title: Castelnuovo's bound and rigidity in almost complex geometry

Abstract: I will discuss the question of whether an energy bound implies a genus bound for pseudo-holomorphic curves in almost complex manifolds. After reviewing what is known in dimensions other than 6, I will talk about a new result in this direction in dimension 6. This result is motivated by an idea of defining new invariants of symplectic Calabi-Yau 6-manifolds. The talk is based on joint work with Thomas Walpuski.

Title: TBA


Past seminars:

Spring 2018
Fall 2017

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