Emmy Noether Lectures

1995 Lecturer: Judith D. Sally

Measuring Noetherian Rings

Judith D. Sally received her BA in mathematics from Barnard College in 1958 and her MA in mathematics from Brandeis University in 1960. The next eight years were devoted mainly to the care and nurturing of three children. In 1968, the year her youngest child began kindergarten, she returned to study in mathematics at the University of Chicago. She received her PhD in 1971, under the direction of Irving Kaplansky. After spending 1971-72 as a postdoctoral visitor at Rutgers University, she was hired as a visiting assistant professor by Northwestern University. The visit lasted a long time! She is currently professor of mathematics there. She received an Alfred P. Sloan Foundation Fellowship in 1977. She spent 1981-82 at Radcliffe College as a Bunting Fellow and 1988-89 at Purdue University under the auspices of the NSF Visiting Professorship for Women Program. She just completed a three-year appointment as algebra editor of the Transactions.
Sally’s research is in Commutative Algebra, one of the fields in which Emmy Noether’s work had such impact. Her main interests lie in the study of Noetherian local rings and graded rings with emphasis on Hilbert functions and birational extensions. These concepts play an important role in ascertaining the nature of singularities in applications in algebraic geometry. The Hilbert function of a local ring at a point on a variety is a very good measure of how bad the singularity is at the point. One of the themes in Sally’s research is the interaction between the local ring and its associated graded ring. This interaction plays a critical role in understanding and computing the Hilbert function. She has also worked on birational blowing up of ideals, the extention of valuations and other concepts in the algebra involved in the resolution of singularities.
Sally enjoys teaching and is pleased with the renewed commitment in the field to undergraduate and graduate teaching. She feels her teaching was revitalized when she began emphasizing active student involvement in class (the syllabus be hanged at times, if necessary!).
In her Noether Lecture, Sally discussed measuring Noetherian rings. Noetherian rings are generally perceived to be the most tractable commutative rings. The well-known finiteness conditions in a Noetherian ring, namely Noether’s ascending chain condition for ideals and the equivalent condition that all ideals are finitely generated, permit interesting finite measures of the “size” and behavior of such rings. However, it is quite surprising that these same finiteness conditions can also force other measures, which might be finite in some non-Noetherian rings, to be infinite.
Sally’s husband, Paul J. Sally, Jr., is Professor of Mathematics at the University of Chicago. At the present time, their eldest son is an assistant professor in the business school at Cornell University, another son is assistant professor in the Slavic department at Stanford University and their youngest son teaches mathematics and computer science at New Trier High School in Winnetka, Illinois. Their seven grandchildren, ages one to seven, have many interesting ideas about their future careers but no definitive plans as yet.