Convexity Seminar

---

Smooth counterexample to Caratheodory conjecture

Speaker: Micah Warren, University of Oregon

Location: Warren Weaver Hall 1314

Date: Tuesday, November 3, 2026, 11 a.m.

Synopsis:

The Caratheodory conjecture from the 1920s states that every closed two dimensional convex surface in three-dimensional space must have at least two umbilic points. This was affirmed for analytic surfaces in the 1940s. Recently Levent Alpoge and John-Paul Smith communicated a document written by Opus 5 containing a smooth counterexample. In this talk I will present a simplified version of the counterexample which should be accessible to anyone with basic understanding of conformal geometry and surface embeddings.