# Young Research Fellow: Philipp Reiser

We are delighted that Dr. Philipp Reiser joins our Cluster as a new Young Research Fellow. He is motivated by the long-standing question of how the topology and geometry of Riemannian manifolds interact. During his stay at Mathematics Münster from 1st to 26th July 2024, he is especially collaborating with Masoumeh Zarei.

Together, they aim to study Riemannian manifolds of non-negative intermediate Ricci curvature. Intermediate Ricci curvature is a family of curvature conditions that interpolates between the classical notions of sectional and Ricci curvature. In particular, they will explore the question of whether there is a bound on the Betti numbers of a closed Riemannian manifold of non-negative intermediate Ricci curvature, which was famously shown by Gromov in the case of sectional curvature. A key ingredient in his proof is Toponogov's angle comparison theorem, which is not expected to hold in the setting of intermediate Ricci curvature. Their strategy includes convergence arguments and understanding the local structure of such spaces by analyzing the distance functions in the context of partial convexity.

Philipp Reiser received his PhD from the Karlsruhe Institute of Technology (KIT) in 2022. Subsequently, he held postdoctoral positions at the Department of Mathematics at the University of Fribourg in Switzerland.

**Link:**

Mathematics Münster's programme for "Young Research Fellows"