Outline of Sottile's course (18 June 2007) ================================================================================= Welcome/Orientation Outline ================================================================================= Week 1: Introduction to algebraic geometry and Groebner bases _________________________________________________________________________________ 23 July Ideals and Varieties _________________________________________________________________________________ 24 July Groebner Bases _________________________________________________________________________________ 25 July Resultants and Bezout's theorem. Done _________________________________________________________________________________ 26 July Solving systems of polynomials Outline Write Demonstrate _________________________________________________________________________________ 27 July Structure of algebraic varieties Outline Write ================================================================================= Week 2: Projective varieties and Toric varieties _________________________________________________________________________________ 30 July Projective varieties Done Type and revise notes _________________________________________________________________________________ 31 July Toric Ideals Done ?Graphic and Code? Type notes _________________________________________________________________________________ 1 August Hilbert Functions and Degree Done, mostly Type notes _________________________________________________________________________________ 2 August Toric varieties Outlined Write _________________________________________________________________________________ 3 August Bernstein's theorem Read Sturmfels Outline Write ================================================================================= 2 August Gale dual systems and bounds in real algebraic geometry Outline. Sketch. Write. (Have graphic example)