What is...?

Tropical enumerative geometry is a branch of combinatorial algebraic geometry that aims to count algebraic objects (usually curves on some surface passing through a number of points) by turning them into combinatorial objects, called tropical curves. Through counting these combinatorial objects, one can then recover their classical algebraic-geometric count. Further, this abstraction allows for extending these counts to other ground fields, particularly the real numbers. In my talk, I'll give an informal introduction to this branch of mathematics, starting by counting curves in (algebraic and tropical) projective space, before talking about how one can adapt these techniques to count curves on other surfaces.