Analysis: From Complex Analysis to PDEs

Assistant Professor Kostyantyn Slutsky

The fusion of descriptive set theory and analysis has given rise to the field of equivariant analysis, which investigates the validity of Borel equivariant versions of classical theorems across various branches of analysis. This talk will highlight key descriptive set-theoretical methods and frameworks essential for proving such Borel equivariant analogs. We provide a detailed examination of two examples from complex analysis: the Weierstrass theorem on the existence of entire functions with specified zeros and the Mittag-Leffler theorem concerning meromorphic functions with prescribed principal parts.
The general framework is also applicable to some classical partial differential equations. Time permitting, we will discuss the existence of Borel equivariant inverses to the Laplacian and explain that the existence of such inverses depends on the dimension of the stabilizers of the arguments.
The new results of this talk were obtained in collaboration with Mikhail Sodin and Aron Wennman.

To participate in this event virtually via Zoom, go to https://uiowa.zoom.us/j/95316149275.