Fall 2018:
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date: 9/12
Organizational and introductory material
Welcome new students!
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date: 9/19
No seminar or classes due to holiday
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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.
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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.
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10/10: Luis Fernandez
Title: Introduction to Kahler manifolds
Abstract:
I will describe foundational material concerning Kahler manifolds.
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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.
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10/24:
Title: TBA
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Past seminars:
Spring 2018
Fall 2017
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