Algorithms in algebraic analysis

Wednesday, January 10, 2007 - 11:15am - 12:15pm
Lind 409
Anton Leykin (University of Minnesota, Twin Cities)
In the first part of this talk I will give an introduction to the algorithmic theory of D-modules. This would include the description of the properties of the rings of differential operators, in particular, the ones that allow for computation of Gröbner bases.

The second part will show the applications of D-modules to the computation of local cohomology of a polynomial ring at a given ideal. The nonvanishing of the local cohomology module of a certain degree may answer the question about the minimal number of generators for the ideal.

The presentation is going to be accompanied by the demonstration of the relevant computations in the D-modules for Macaulay 2 package.