SEMINAR on Integrable Systems and Geometry

[Emanuele Tuillier Illingworth]

SEMINAR on Integrable Systems and Geometry


Speaker: Chaya Norton, CRM Montreal

Title: Moduli of Curves and Differentials with Real Periods

Friday, February 27, at 11:00.
SISSA, Room 136

Abstract: We will discuss the behavior of differentials with real 
periods near the boundary of the Deligne-Mumford compactification of the 
moduli space of curves overcoming the difficulty that such differentials 
may vanish identically on some irreducible components. The description 
of such differentials near nodal curves allows one to track zeros of the 
differentials under degeneration of the curve, showing the limit of 
zeros is parametrized by products of real projective spaces, one for 
each node. The degeneration techniques developed provides a tool for 
understanding common zeros of such differentials which has applications 
to the study of the geometry of the moduli space of curves, as was 
pointed out in recent work of Grushevsky and Krichever.