October 4 - 9, 2010
AAC Mini Course
Computing in Commutative Algebra
Professor Dr Gerhard Pfister
(University of Kaiserslautern, Germany)
For Prof. Pfister's very short CV click here
Attention! The notes of this mini course are available here.
First lecture: Gröbner bases and SINGULAR
Monday, October 4, 2010, 10-10:50 a.m., C-2010
The notion of a Gröbner basis (with respect to any ordering) will be explained as the basis for computations in localizations of factor-rings of polynomial rings. The computer algebra system SINGULAR and its use will be explained as a basis for further applications in commutative algebra and other fields.
Second lecture: Polynomial solving and primary decomposition
Tuesday, October 5, 2010, 10-10:50 a.m., SN-3060
Triangular sets as a symbolic pre-processing to solve polynomial systems of equations will be discussed. The computation of a primary decomposition – one of the most difficult task in computer algebra – will be explained. The computation of the normalization of a ring will be included.
Third lecture: Invariants
Thursday, October 7, 2010, 10-10:50 a.m., A-1049
The computation of many invariants in commutative algebra as Hilbert function, Hilbert polynomial, dimension, degree, multiplicity will be discussed and explained.
Fourth lecture: Homological Algebra
Friday, October 8, 2010, 10-10:50 a.m., SN-3060
Important notions in homological algebra as for instance depth and Cohen-Macaulayness will be analyzed and it will be explained how to check and respectively compute it.
Discussions and Coffee after each lecture in AAC room HH-2010