**Date & Time:** Tuesday, April 15, 2014, 16:00-17:00.

**Venue:** Ramanujan Hall

**Title:** Prime ideals in Noetherian Ring

**Speaker: ** Sylvia Wiegand, University of Nebraska

**Abstract:** Let R be a commutative Noetherian ring. We consider the set Spec(R) of the prime ideals of R as a poset ordered by inclusion. Around 1950, Kaplansky asked " which posets arise as Spec R for a Noetherian ring R ?" This question is still completely open, even when restricted to two-dimensional integral domains, despite a large amount of work done over the intervening years by Hochster, Heitmann, McAdam, Nagata, Ratliff and R. Wiegand.

In this talk, we give some general results and examples. Our primary focus is more recent results concerning prime spectra of two dimensional polynomial and power series rings. These results have been obtained with William Heinzer, Christel Rotthaus, Ela Celikbas and Christina Eubanks-Turner.