Machine learning in algebraic geometry: some examples

The use of machine learning in pure mathematics to help formulate conjectures has been a growing research area, with examples in knot theory and representation theory. In this talk, we go through two successful example applications of machine learning algorithms to problems in algebraic geometry where toric varieties are the central object of study. In the first, we study the quantum period of toric varieties, and see if we can learn their dimension from it. In the second, we construct a neural network that distinguishes between terminal and non-terminal toric varieties from their GIT data, which motivates a proposed mathematical solution to the problem.