Stability of associated primes of monomial ideals

A recurring topic in mathematics is to decompose objects into smaller, better understood parts. For example, every natural number can be decomposed into a product of prime numbers. The Lasker-Noether Theorem (1904, 1921) states that any ideal in a Noetherian ring can be decomposed into primary ideals. This allows to associate a unique set of prime ideals to every ideal, the so-called associated primes. It is known that the sequence of the set of associated primes of powers of monomial ideals stabilizes at some point: the stability index. This talk will introduce approaches to derive an upper bound for this stability index.