Takagi lectures on Donaldson-Thomas theory

TL;DR

This paper summarizes Takagi's 2017 lectures on Donaldson-Thomas theory, covering its fundamentals, origins, open questions, and recent advances in counting curves in algebraic threefolds.

Contribution

It provides a comprehensive overview of DT theory, highlighting recent developments and open problems in the field.

Findings

Discussion of fundamental concepts of DT counts

Overview of recent advances in DT theory

Identification of open questions in the field

Abstract

These are the notes for my 2017 Takagi lectures on DT counts of curves in algebraic threefolds. We discuss the fundamentals of the subject, its origins, open questions, and certain recent advances.