CMSA Member Seminar: How complex is S^6?

A longstanding problem posed by Hopf in 1948 asks which even-dimensional spheres can be equipped with complex structures. Classical results show that only S^2 and S^6 can admit a complex structure. Since S^2 has its own standard complex structure, the question was only open for S^6. After explaining the basics and significance of this problem, we discuss the recent manuscript produced by Claude under the direction of Levent Alpöge, which constructs a one-parameter family of complex structures on S^6. We also discuss related open problems in the field and possible directions for future research.

Lunch will be provided.