Colloquium: Tuesday Nov. 25, 2025 (14:00, room 614). Speaker: Boris Shapiro (Stockholm). Title: “Return of the plane evolute”.
We consider the evolutes of plane real-algebraic curves and find lower bounds for the following 4 quantities:
(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 crunodes which can occur on the dual curve to the evolute of a real-algebraic curve of degree d;
(4) the maximal number of crunodes which can occur on the evolute of a real-algebraic curve of degree d.
