SPEAKER:  Daniel Litt (University of Georgia)

TITLE:  The Section Conjecture at the Boundary of Moduli Space

ABSTRACT:  Grothendieck's section conjecture predicts that over arithmetically interesting fields (e.g. number fields or p-adic fields), rational points on a smooth projective curve X of genus at two can be detected via the arithmetic of the etale fundamental group of X. We construct infinitely many curves of each genus satisfying the section conjecture in interesting ways, building on work of Stix, Harari, and Szamuely. The main input to our result is an analysis of the degeneration of certain torsion cohomology classes on the moduli space of curves at various boundary components. This is (preliminary) joint work with Padmavathi Srinivasan, Wanlin Li, and Nick Salter.