Wojciech Kucharz

Title: Introduction to regulous geometry

Abstract: 
A real-valued function on R^n is said to be k-regulous, where k is a nonnegative integer,
if it is of class C^k and can be represented as a quotient of two polynomial functions on R^n.
Several interesting results involving such functions have been obtained recently. They include a
variant of the classical Nullstellensatz for the ring of k-regulous functions on R^n, a description of
the zero locus of an arbitrary collection of k-regulous functions in terms of Zariski constructible
sets, and counterparts of Cartan's theorems A and B for quasi-coherent k-regulous sheaves. The talk
will focus on these and other results leading to the development of regulous geometry.