## A lecture at the Mathematical Colloquium of the Institute of Mathematics

The Institute of Mathematics at the Faculty of Mathematics and Physics invites everybody to participate in the lecture

## Local Uniformization, defect and associated graded rings

by

### prof. Steven Dale Cutkosky

University of Missouri, USA

**Abstract:**

We begin by giving an overview of Abhyankar’s approach to local uniformization (resolution of singularities along a valuation) and the role of defect in an extension of valued fields as an obstruction to local uniformization.

We discuss how defect can be detected through lack of finite generation of extensions of associated graded rings along the valuation. We then raise a question on eventual finite generation of extensions of associated graded rings in defectless extensions, which we answer positively in dimension two and equicharacteristic zero.

The lecture will take place on June 21, 2018 at 16.00 in the room 212 in the faculty building.