Title: Harmonic Maps between Round Spheres: Hopf Invariants and Factorization
Speaker: Guo Qi (Renmin University of China)
Time: Friday , October 30, 2026, 17:00-18:00
Venue: Gewu Building, Room 315
Abstract:
The Hopf fibration provides a fundamental model for harmonic maps from the round three-sphere to the round two-sphere. Two closely related questions arise: which homotopy classes admit smooth harmonic representatives when both metrics are fixed to be the standard round metrics, and when must such representatives factor through a Hopf fibration?
In this talk, I will discuss recent work on these questions, with particular emphasis on an approach to constructing smooth harmonic maps with arbitrary prescribed integer Hopf invariant. I will outline the main steps of the existence argument, explain how variational method and topology enter the construction, and discuss the implications for Hopf factorization. Particular attention will be given to the distinction between finding a harmonic representative in a homotopy class and determining whether all harmonic maps in that class share the same geometric structure.
