Abstract: We will start this talk with an introduction to Donaldson–Thomas (DT) theory. DT theory counts ideal sheaves to answer questions starting “how many curves on the 3 dimensional variety X…”. We will look at a linear system as a simple example of sheaf counting. We will then discuss the general DT construction, its relationship to Gromov–Witten theory and a handful of interesting results.
Subject to time, we explain why a logarithmic Donaldson–Thomas theory should prove useful. We discuss the logarithmic linear system as a simple example of logarithmic Donaldson–Thomas spaces. The example will show how solving a tropical moduli problem solves an algebraic moduli problem for free.