Math 765 - Computational Commutative Algebra

January 9 - Monomial Orders and Multivariate Polynomial Division Getting Started Multivariate Polynomial Division January 11 – Groebner Bases and Buchberger's Algorithm Groebner Bases Buchberger's Algorithm January 14 – An Introduction to Macaulay2 Sample Macaulay2 Session January 16 – Introduction to Affine Algebraic Geometry Affine Varieties Groebner Bases and Elimination Ideals January 18 – First Macaulay2 Hands-On Session Problem 1 Problem 2 Problem 3 January 23 - R-modules January 25 - More on Graded Modules, Minimal Free Resolutions, Betti Numbers January 28 - Betti Diagrams, The Koszul Complex for R/m, Proof of Hilbert Syzygy Theorem January 30 - Projective Geometry, Hilbert Functions February 1 - Worksheet 2 February 4 The Hilbert Function, Series, and Polynomial February 6 - Algorithms for minimal free resolutions More general terms orders: February 8 Schreyer Resolutions and Schreyer Frames February 11 - Example of Computing a Schreyer Frame February 13 - Example of Computing a Schreyer Resolution February 15 - An Algorithm for Computing a Schreyer Resolution February 18 February 20 - Worksheet Day February 22 - More on Hilbert Functions, Points in Projective Space Geometric Information from the Hilbert Function February 25 - Points in Projective Space, Regularity, Resolutions, Examples Imposed Conditions February 27 - Some background towards (stating and) proving the theorem March 1 - Worksheet Day - Writing your own Macaulay2 functions. March 4 - Regularity, Depth, and Local Cohomology Local Cohomology March 6 March 8 March 18 Completing the Proof from Last Time: Applications of the theorem: March 20 March 22: Loading Packages, Depth in Macaulay2 Problem 1 Problem 2 Week of March 25 - 29: Simplicial Complexes Worksheet Problem 1 Problem 2 Problem 3 Problem 4 Week of April 1: Alexander Duality Problem 1 Problem 2 Problem 3