• Mathematics Department Colloquium
• SAS 4201, 4:15-5:15pm, March 23, 2026
• Dr. Andrew Sageman-Furnas, NC State
• Discovering Isometric Tori with The Sam Curvatures

Abstract: A longstanding problem in differential geometry, known as the Bonnet problem, asks: is a compact surface in Euclidean three-space uniquely determined by its metric and mean curvature function? The answer is known to be yes for a topological sphere and yes for a generic surface. In this talk, we explicitly construct a pair of immersed tori that are related by a mean curvature preserving isometry. These tori are the first examples of compact Bonnet pairs. Moreover, we prove these isometric tori are real analytic. This resolves a second longstanding open problem on whether real analyticity of the metric already determines a unique compact immersion. We describe the discovery of these analytic tori using discrete differential geometry. It involves exploring immersions of a 5×7 quad decomposition of a torus and a theory of discrete Bonnet pairs. The smooth/analytic theory is joint work with Alexander Bobenko and Tim Hoffmann, and the discrete theory is joint work with Tim Hoffmann and Max Wardetzky.

Andrew Sageman-Furnas studies discrete differential geometry and its applications across the sciences, arts, and mathematics. He joined NC State as an Assistant Professor in 2021, after a postdoc at the Technical University of Berlin. Andy received his PhD in Mathematical Sciences from the University of Göttingen and masters degrees in Textiles from the University of Leeds.