# Gerhard Pfister

**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 decompositionTuesday, 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:InvariantsThursday, 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 AlgebraFriday, 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