# Algebraic Geometry Seminar

#### Tautological Relations Via the Abel--Jacobi Map

**Speaker:**
Dmitry Zakharov , Courant Institute of Mathematical Sciences

**Location:**
Warren Weaver Hall 317

**Date:**
Tuesday, September 10, 2013, 3:30 p.m.

**Synopsis:**

Given a curve with marked points and integer weights on the markings, we consider the corresponding divisor. This defines an Abel--Jacobi map from the moduli space of marked curves to the universal Jacobian variety. This map extends to the space of curves of compact type. Pulling back relations from the universal Jacobian for various values of the weights gives a plethora of tautological relations on the space of curves of compact type. These relations include those discovered by Faber, Getzler, Belorousski and Pandharipande, and Tavakol.