Jessica Sidman,
The ideal membership problem, bounds, and Castelnuovo-Mumford Regularity

This will be an expository talk based on a paper of Ernst Mayr and Albert Meyer. I will outline how their work gives a lower bound on the computational complexity of the polynomial ideal membership problem in which one gives polynomials g and f_1,..., f_k and asks if g is in the ideal generated by the f_i. If time permits I will also sketch how their work is related to bounds on Castelnuovo-Mumford regularity.