# Markus Wolff: Ricci-Flow on surfaces along the standard light cone in the $3+1$ Minkowski spacetime

**Time: **
Thu 2023-11-09 10.15 - 11.15

**Location: **
3721, Lindstedtsvägen 25

**Language: **
English

**Participating: **
Markus Wolff, KTH

Identifying any conformally round metric on the $2$-sphere with a unique cross section on the standard lightcone in the $3+1$-Minkowski spacetime, we gain a new perspective on $2d$-Ricci flow on topological spheres. It turns out that in this setting, Ricci flow is equivalent to a null mean curvature flow first studied by Roesch–Scheuer along null hypersurfaces. Exploiting this equivalence, we can translate well-known results from $2d$-Ricci flow first proven by Hamilton into a full classification of the singularity models for null mean curvature flow in the Minkowski lightcone. Conversely, we obtain a new proof of Hamilton’s classical result using only the maximum principle.