Vorträge in der Woche 13.10.2025 bis 19.10.2025
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Mittwoch, 15.10.2025: Combinatorial patchworking of real algebraic hypersurfaces using triangulations dilated by two
Alois Demory (Tuebingen)
Combinatorial patchworking is a tool that allows one to construct real algebraic hypersurfaces with prescribed topological properties of their real part, starting from a triangulation of a polytope whose vertices are endowed with some signs. First introduced in the early 80s by O. Viro, it has proven to be extremely fruitful, and understanding what real algebraic hypersurfaces can or cannot be constructed using this tool has become an important question. The vast majority of the knowledge we currently have about this problem is restricted to the case where the considered triangulations are unimodular. In this talk, we discuss some recent developments concerning a different class of triangulations: triangulations that are obtained by dilating a triangulation by two.
| Uhrzeit: | 10:15 - 11:15 |
| Ort: | S10 |
| Gruppe: | Oberseminar kombinatorische algebraische Geometrie |
| Einladender: | Daniele Agostini, Hannah Markwig |
Donnerstag, 16.10.2025: Curve Shortening Flow on a Surface with Ricci Flow Background
Tejal Bhattarai (Tübingen)
We will study the evolution of embedded closed curves by a curve shortening flow on a smooth closed surface whose background metric evolves by the volume-normalized Ricci flow. We consider the ratio of extrinsic and intrinsic distances along the curve and show that under this coupled flow, this ratio can deteriorate at most exponentially at local minima. For curves that survive for infinite time, using integral estimates, we show that the curvature and all its higher derivatives converge to zero. As an application, we consider the evolution of curves foliating the topological two-sphere and show that there exists exactly one curve that survives the coupled flow for infinite time and smoothly (sub)converges to a great circle on the round sphere.
| Uhrzeit: | 14:00 - 15:00 |
| Ort: | C9A03 |
| Gruppe: | Oberseminar GADR |
| Einladender: | Cederbaum, Huisken, Metzger (Potsdam) |