# Lecture series

## by Graeme Wilkin (Assistant Professor of Mathematics, NUS, Singapore)

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Lectures on Morse Theory and applications

## About the IGA Lecturer:

Graeme Wilkin is from Tasmania. He completed his undergraduate studies at Melbourne University, and his PhD from Brown University. He held postdoc positions at John Hopkins University and at the University of Colorado at Boulder, after which he took up an Assistant Professor position at NUS, Singapore where he is at currently.

## Abstracts of lectures (6 hours in length) and venue:

Lecture 1: Introduction to Morse theory

I will introduce the basics of Morse theory and give many examples to illustrate the theory. I will also touch on some generalisations of Morse theory due to Bott, Palais, Smale, Atiyah & Bott and Kirwan, and their applications.

Engineering & Maths EMG06 - Wednesday 11th July - 3-5pm

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Lecture 2: Flow lines and the Morse complex

Modern interpretations of Morse theory use flow lines between critical points to obtain more information about the underlying manifold. In this lecture I will explain how to use flow lines to construct a Morse complex which computes the de Rham cohomology of a manifold.

Engineering & Maths EMG06 - Wednesday 18th July - 3-5pm

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Lecture 3: Morse theory on singular spaces

In the final lecture I will talk about my recent work to develop a Morse theory for singular spaces, and describe some applications to moduli spaces of quivers with relations.

Engineering & Maths EMG06 - Wednesday 25th July - 11 - 1pm

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