Special Geometry Seminar: April 13, 2026
Monday, April 13, 2026 | SC1310 4:00pm to 5:00pm
Speaker: Richard Hain (Duke University)
Title: Hyperelliptic Johnson homomorphisms and higher algebraic cycles
Abstract: In this talk I will define analogues of the Johnson homomorphism for hyperelliptic mapping class groups and explain their relevance to the study of higher algebraic cycles associated to hyperelliptic curves. The talk will focus mainly on the topology and be relatively elementary.
After a review of the classical Johnson homomorphism, I will define hyperelliptic mapping class groups and the associated Johnson homomorphisms. Several related conjectures and open questions will be stated. The talk will conclude with a discussion of the connection between hyperelliptic Johnson homomorphisms, the cohomology of moduli spaces of hyperelliptic curves, and its implications for algebraic cycles associated to hyperelliptic curves.