## EVENT DETAILS AND ABSTRACT

**Algebraic Geometry Seminar**
**Title:** Rational curves on fibered Calabi-Yau manifolds

**Speaker:** Diletta Martinelli

**Speaker Info:** Univ. of Edinburgh

**Brief Description:**

**Special Note**:

**Abstract:**

Calabi-Yau manifolds are of interest in both algebraic geometry and theoretical physics. In particular the problem of determining whether Calabi-Yau manifolds do
contain rational curves has big relevance in string theory. Moreover, a folklore conjecture in algebraic geometry predicts the existence of rational curves on every Calabi-Yau manifolds. There are several positive answers in dimension three but very little
is known in higher dimension. I will talk about a joint work with Simone Diverio and Claudio Fontanari where we prove the existence of rational curves on Calabi-Yau manifolds of any dimension that admit an elliptic fibration. If time permits, I will show how
to use this result to produce rational curves on Calabi-Yau manifolds that admit a fibration onto a curve whose fibers are abelian varieties.

**Date:** Tuesday, October 24, 2017

**Time:** 4:00pm

**Where:** Lunt 107

**Contact Person:** Mihnea Popa

**Contact email:** mpopa@math.northwestern.edu

**Contact Phone:**

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