3:30 pm, Lecture Hall 1
Tropical structures in algebraic geometry
University of Cambridge.
In the last decade, tropical geometry has emerged as a systematic method of translating questions in algebraic geometry into (sometimes impossible) combinatorics. The basic premise of the subject is to study algebraic varieties through polyhedral skeletons", which capture only a fraction of the complexity of the variety, but are amenable to manipulation and computation.The roots are varied, ranging from symplectic geometry, to mirror symmetry and string theory, to non-archimedean analysis, and beyond. I will give an overview of the subject, with a focus on the nature of the methods involved rather than the technicalities. In order to keep the mathematics grounded, I will focus on one application to the following question: In how many ways can you write equations for a compact Riemann surface?
** This talk will be accessible to students! My goal is that anyone who knows what a Riemann surface/algebraic curve is should get something out of the talk.