Piene & Shapiro: Return of the plane evolute

Date: 2023-06-28

Time: 11:00 - 12:00

Zoom link: https://kva-se.zoom.us/j/9217561880

Speakers

Ragni Piene, University of Oslo / Boris Shapiro, Stockholm University

Abstract

We consider the evolutes of plane real-algebraic curves and discuss some of their complex and real-algebraic properties. In particular, for a given degree d ≥ 2, we provide lower bounds for the following four numerical invariants: 1) the maximal number of times a real line can intersect the evolute of a real-algebraic curve of degree d; 2) the maximal number of real cusps which can occur on the evolute of a real-algebraic curve of degree d; 3) the maximal number of (cru)nodes which can occur on the dual curve to the evolute of a real-algebraic curve of degree d; 4) the maximal number of (cru)nodes which can occur on the evolute of a real-algebraic curve of degree d.