ABHYANKAR 82nd BIRTHDAY CONFERENCE SPEAKER: Sylvia Wiegand (Nebraska) TITLE: Examples of integral domains inside power series rings ABSTRACT: I will speak on joint work with Heinzer and Rotthaus on a technique for constructing examples using power series. For R a Noetherian ring, the constructed rings are either (1) an intersection $A=S\cap L$ of a power series ring S over R with a field L between the field of fractions of R and the total quotient ring of S, or (2) a certain nested union B of polynomial rings $B_i=R[\tau_{i1},\dots,\tau_{In}]$ over R, where for each $i$ the $\tau_{ij}$ are elements of S that are algebraically independent over R. Certain flatness conditions imply that the two rings A and B are equal, or that they are both Noetherian and equal. We describe specific examples as time permits.