Jump to present
semester
Spring 2018:
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1/31
Organizational and introductory material
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2/7: Luis Fernandez
Almost complex structures on six-sphere through octonions
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2/14: Bora Ferlengez
Almost complex structures on six-sphere through octonions (continued)
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2/21: Luis Fernandez
Non-integrable ACS on six-sphere
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2/28: Luis Fernandez
Metric on the space of ACS on six-sphere (continued)
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3/7,3/14,3/21: no meeting
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3/28: Aleksandar Milivojevic (Stony Brook University)
Relations among Hodge numbers on a hypothetical complex six-sphere
Notes
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3/29: Spiro Kargiannis (U. of Waterloo)
Cohomologies on almost complex manifolds and their applications
Abstract:
We define three cohomologies on an almost complex manifold (M, J), defined
using the Nijenhuis-Lie derivations induced from the almost complex structure
J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of
these can be applied to distinguish non-isomorphic non-integrable almost
complex structures on M. Another one, the J-cohomology, is familiar in the
integrable case but we extend its definition and applicability to the case of
non-integrable almost complex structures. The J-cohomology encodes whether a
complex manifold satisfies the "del-delbar-lemma", and more generally in the
non-
integrable case the J-cohomology encodes whether (M, J) satisfies a
generalization of this lemma. We also mention some other potential
cohomologies on almost complex manifolds, related to an interesting question
involving the Nijenhuis tensor.
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4/18: Aleksandar Milivojevic (Stony Brook University)
Relations among Hodge numbers on a hypothetical complex six-sphere (part 2)
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4/25: Joining Simons mathfest 2018
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5/2: Scott Wilson
Results concerning almost complex structures on the six-sphere(1)
This is an exposition of the work in arxiv:1610.0920
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5/9: Scott Wilson
Results concerning almost complex structures on the six-sphere(2)
This is a continuation of the previous talk.
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5/16: Luis Fernandez
No orthogonal almost complex structure is integrable on six-sphere
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