Monday, November 13, 2006 - 11:15am - 12:15pm
It is well-known that on the one hand the costs for computing a Gröbner basis can be prohibitively high in the worst case, but on the other hand computations can often be carried out successfully in practice. As an attempt to explain this discrepancy, several invariants that measure the size or the complexity of an ideal or a module have been introduced. The most prominent one is the Castelnuovo-Mumford regularity, but there are also extended degrees introduced by Vasconcelos and, more recently, the extended regularity jointly proposed with Chardin. The latter two notions are defined axiomatically. In the talk we will discuss the three concepts and their relations as well as some known results and open problems.