Title    name
Tropical Geometry
 
  Title
  Speaker Bend Strumfels
  Date 2009-06-15
  Host
  Place KIAS
  File  의 1 번째 Real Media 동영상입니다.
 
Abstract : 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.