Initially regular sequences.
Abstract: An important invariant in commutative algebra is that of the depth of a module. We are particularly interested in depth R/I^t, where I is a homogeneous ideal in a polynomial ring R and t is in N. In general, the depth of the module R/I^t is measured by the maximal length of an m-regular sequence on R/I^t, where 'm' is the homogeneous maximal ideal of R. During this talk we will discuss the notion of initially regular sequences. These sequences have similar properties as regular sequences and provide improved bounds on depth R/I. We will also give concrete ways to construct these type of sequences. This is joint work with T\`{a}i H\`{a} and Susan Morey