Title    name Lastest   |   Most hits   년도선택 최근 50건20132012201120102009200820072006200520042003200220012000     Tropical Geometry Lecture 10 : Tropical Discriminant Bernd Sturmfels (University of California, Berkeley) 2009-06-19     Tropical Geometry Lecture 9 : Counting Curves Bend Strumfels (University of California, Berkeley) 2009-06-19     Tropical Geometry Lecture 8 : What is the rank of a matrix ? Bend Strumfels (University of California, Berkeley) 2009-06-18     Tropical Geometry Lecture 7 : Morphims and Secant Varieties Bend Strumfels (University of California, Berkeley) 2009-06-18      Tropical Geometry Lecture 6 : Grassmannians Bend Strumfels (University of California, Berkeley) 2009-06-17     Tropical Geometry Lecture 5 : Matroids and Linear Spaces Bend Strumfels (University of California, Berkeley) 2009-06-17     Tropical Geometry Lecture 4 : The Fundamental Theorem Bend Strumfels (University of California, Berkeley) 2009-06-16     Tropical Geometry Lecture 3 : Fields and Polyhedra Bend Strumfels (University of California, Berkeley) 2009-06-16     Tropical Geometry Lecture 2 : Eigenvalues and Eigenvectors Bend Strumfels (University of California, Berkeley) 2009-06-15     Tropical Geometry Lecture 1 : Elementary Introduction Bend Strumfels (University of California, Berkeley) 2009-06-15   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.

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