SMS scnews item created by Catherine Meister at Fri 6 Mar 2026 1055
Type: Seminar
Distribution: World
Expiry: 20 Mar 2026
Calendar1: 12 Mar 2026 1300-1400
CalLoc1: SMRI Seminar Room (A12 Macleay Room 301)
Auth: cmeister@159-196-153-133.9fc499.syd.nbn.aussiebb.net (cmei0631) in SMS-SAML

SMRI Seminar

Mapping class groups and algebraic cycles

Hain

Mapping class groups and algebraic cycles

Richard Hain, Duke University

SMRI Seminar, Thursday 12th March, 2026, 1 pm – 2 pm, SMRI Seminar Room (A12 Macleay Room 301)

Abstract: The topology, geometry and arithmetic of moduli spaces of curves are well known to be intertwined. Many geometric properties of algebraic curves are reflected in the topology and geometry of the corresponding moduli space. In this talk I will give an overview of one aspect of this connection --- namely results that relate algebraic cycles on powers C^n of a genus g curve C to the structure of the mapping class group of a closed surface of genus g. This is a subject with a rich history with roots in the work of Riemann and Abel in the 19th century.
I will review relevant background material, including the definition of and basic results about mapping class groups and algebraic cycles. I will explain why cycles that are defined for all curves, such as those defined by Ceresa and Gross--Schoen, are related to the Torelli subgroups of mapping class groups. If time permits, I will describe a new (higher) algebraic cycle defined for hyperelliptic curves that Wanlin Li and I have constructed.

For seminar updates, see our What's On Calendar. Please join us after the seminar for the SMRI afternoon tea, every Thursday at 2 pm on the SMRI Terrace.

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