Differential Geometry Seminar: Holomorphic and algebraic immersed curves directed by a flexible cone

Speaker: Finnur Larusson (University of Adelaide)

Title: Holomorphic and algebraic immersed curves directed by a flexible cone

Date: Friday 4 April 2025, 12:10pm in Benham G25 Peter Martin Room

Abstract: I will describe recent joint work with Antonio Alarcon (Crelle 2025) and Alarcon and Franc Forstneric (arXiv 2024). We investigate immersed complex curves in complex affine space, directed by a cone A satisfying one of the flexibility properties that are studied in Oka theory. When A is the so-called null quadric, such curves play a fundamental role in the theory of minimal surfaces. There are other important examples.  We are interested in approximation and interpolation theory for such curves, as well as the "rough shape" of the space of all curves. I will review results from 5-10 years ago in the holomorphic case and then describe our recent results in the algebraic setting, where obstacles not present in the holomorphic case arise.