Spring 2018:

1/31
Organizational and introductory material

2/7: Luis Fernandez
Almost complex structures on sixsphere through octonions

2/14: Bora Ferlengez
Almost complex structures on sixsphere through octonions (continued)

2/21: Luis Fernandez
Nonintegrable ACS on sixsphere

2/28: Luis Fernandez
Metric on the space of ACS on sixsphere (continued)

3/7,3/14,3/21: no meeting

3/28: Aleksandar Milivojevic (Stony Brook University)
Relations among Hodge numbers on a hypothetical complex sixsphere
Notes

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 NijenhuisLie derivations induced from the almost complex structure
J and its Nijenhuis tensor N, regarded as vectorvalued forms on M. One of
these can be applied to distinguish nonisomorphic nonintegrable almost
complex structures on M. Another one, the Jcohomology, is familiar in the
integrable case but we extend its definition and applicability to the case of
nonintegrable almost complex structures. The Jcohomology encodes whether a
complex manifold satisfies the "deldelbarlemma", and more generally in the
non
integrable case the Jcohomology 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.

4/18: Aleksandar Milivojevic (Stony Brook University)
Relations among Hodge numbers on a hypothetical complex sixsphere (part 2)

4/25: Joining Simons mathfest 2018

5/2: Scott Wilson
Results concerning almost complex structures on the sixsphere(1)
This is an exposition of the work in arxiv:1610.0920

5/9: Scott Wilson
Results concerning almost complex structures on the sixsphere(2)
This is a continuation of the previous talk.

5/16: Luis Fernandez
No orthogonal almost complex structure is integrable on sixsphere
