# Algebraic Geometry Seminar

#### Moduli of Curves and Differentials with Real Periods

**Speaker:**
Chaya Norton, University of Montreal

**Location:**
Warren Weaver Hall 201

**Date:**
Tuesday, November 18, 2014, 3:30 p.m.

**Synopsis:**

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, showing the limits of zeros is parametrized by product 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 for the study of the geometry of moduli space of curves, as was pointed out in the recent work of Grushevsky and Krichever.