Lángi Zsolt: Monotonicity of the isoperimetric ratio in the Eikonal model 

In the past decades, finding monotone quantities under various geometric
PDEs has been in the focus of research. In this talk we investigate such
a problem,
and show that under the Eikonal abrasion model, which prescribes uniform
normal speed in the direction of the inward surface normal, the
isoperimetric quotient of a convex body is decreasing monotonically.
The proof os based on tools from Brunn-Minkowski theory. The result may
provide a possible explanation for the elongated shape of the extrasolar
asteroid 'Oumuamua. Joint work with Gábor Domokos.