GTA Seminar | Speaker: Ilka Agricola (Philipps-Universitaet Marburg, Germany)

Title: The Hopf problem on the six-sphere

Abstract: In this survey talk, I will outline the history of the problem of proving or disproving the existence of complex structures on S⁶ and explain why this question is interesting. It goes back to a 1947 paper by Heinz Hopf. Moreover, I will explain the rich structure of S⁶ as an almost complex manifold, and how it relates to the exceptional Lie group G₂ , octonions, and spin geometry.