Algebraic Geometry Seminar: Malabika Pramanik (UBC)

The structure of the zero set of a multivariate polynomial is a topic of wide interest, in view of its ubiquity in problems of analysis, algebra, partial differential equations, probability and geometry. The study of such sets originated in the pioneering work of Jung, Abhyankar and Hironaka and has seen substantial recent advances in an algebraic setting.

In this talk, I will mention a few situations in analysis where the study of polynomial zero sets plays a critical role, and discuss prior work in this analytical framework in two dimensions. Our main result (joint with Tristan Collins and Allan Greenleaf) is a formulation of an algorithm for resolving singularities of a real-analytic function in any dimension with a view to applying it to a class of problems in harmonic analysis.