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.

Spring 2019:

1/30: Matthew Cushman
Title: Introduction to Chern-Weil theory.

Abstract: We discuss the Weil homomorphism for principal bundles, from invariant functions on the Lie algebra to characteristic forms on the base.

2/6: Matthew Cushman
Title: Transgression of characteristic forms and the Bott homomorphism

Abstract: We will discuss fiber integration and a generalization of the Weil homomorphism which gives secondary characteristic classes.

2/13: Prof. Luis Fernandez (Bronx, CUNY)
Title: Computing examples of the Cirici-Wilson spectral sequence using Mathematica.

Abstract: I will explain the workings of, and do some examples with, a Mathematica notebook I recently created to calculate the first two pages of a spectral sequence on some examples of almost complex manifolds.

2/20: Scott Wilson
Title: The de Rham complex of a complex manifold.

Abstract: A linear operator on a vector space can be extended to the exterior algebra either as a derivation, or as an algebra map. In the case of an almost complex structure (operating on the complexified cotangent space of a manifold) these two choices can be used to encode the integrability condition, in terms of a compatibility with the exterior differential. This simplifies some interesting Lie theory. One can similarly (try to) extend complex conjugation in two ways. I will share some partial progress towards extending this algebra to a representation of sl(2,R) which is mirror-dual to Lefschetz's construction, the latter of which plays an important role for symplectic manifolds with compatible metrics.

3/27: Caner Koca (City Tech, CUNY)
Title: TBA

Abstract: TBA

Past seminars:

Fall 2018
Spring 2018
Fall 2017

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