Tropical Geometry is a piecewise-linear version of algebraic geometry, where the underlying arithmetic is based on the min-plus algebra. This series of ten lectures gives an introduction to this subject, with emphasis on drawing pictures and on algorithms for passing back and forth between classical and tropical objects.
After a brief introduction to tropical varieties, we shall discuss linear spaces and convex polytopes in the tropical world, and we examine what happens to classical notions from linear algebra (matrix rank, nullspace, eigenvalues). Determinantal varieties and Grassmannians will make a prominent appearance. We also present tropical elimination theory, with a certain focus on discriminants and resultants, as well as work of Mikhalkin and others on tropical moduli spaces and computing Gromov-Witten invariants. The material to be covered is drawn from a book manuscript by the
speaker and Diane Maclagan.
The meeting is hosted by the Korea Institute for Advanced Study (KIAS), Korea, and co-sponsored by the KIAS and the KMS.