Program
Kyler Siegel (Southern California)
Multidirectional tangency constraints
Abstract: Cramer's theorem from 1750 is a beautiful illustration of enumerative geometry: there is exactly one curve in the plane if we impose the right number and type of constraints. More recently, the last few decades have seen an explosion of new enumerative problems and solutions, building on deep ideas in algebraic geometry, symplectic geometry, and string theory. In this talk I will introduce a new type of constraint which can be described with only classical mathematics but whose study involves modern tools like Gromov-Witten theory and symplectic field theory. Without assuming any background in these topics, I will try to convey the flavor of these new enumerative problems, including why they are interesting and how to approach them.