Nonpositive curvature is not coarsely universal

A complete geodesic metric space of global nonpositive curvature in the sense of Alexandrov is called a Hadamard space. In this talk we will show that there exist metric spaces which do not admit a coarse embedding into any Hadamard space, thus answering a question of Gromov (1993). The main technical contribution of this work lies in the use of metric space valued martingales to derive the metric cotype 2 inequality with sharp scaling parameter for Hadamard spaces. The talk is based on joint work with M. Mendel and A. Naor.

• Speaker: Alexandros Eskenazis (Princeton)
• Tuesday 30 October 2018, 14:00–15:00
• Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
• Series: Probability; organiser: Perla Sousi.