## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**Title:** The directed Fukaya category and Morse theory

**Speaker:** Joseph Johns

**Speaker Info:** Univesity of Chicago

**Brief Description:**

**Special Note**:

**Abstract:**

Let $f: N \longrightarrow \mathbb{R}$ be a Morse function and let $g$ be a Riemannian metric so that $(f,g)$ is
Morse-Smale. Given this data I will explain how to construct
an explicit model of a Lefschetz fibration $\pi = \pi_{(f,g)}: T^*N \longrightarrow \mathbb{C}$ which extends $f$
and has no further critical points. I will then relate the directed Fukaya category of $\pi$ to the flow category
of $(N,f,g)$. If time permits, I will mention an application of these results to Arnold's nearby Lagrangian
problem, building on work of Fukaya, Smith, and Seidel.

**Date:** Thursday, January 12, 2006

**Time:** 4:00pm

**Where:** Lunt 107

**Contact Person:** Prof. Chiu-Chu Melissa Liu

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

**Contact Phone:** 847-467-1874

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