Giancarlo Urzúa, Wormholes: MMP, Topology, Continued Fractions

We defined wormholes in https://arxiv.org/abs/2102.02177 (joint with Nicolás Vilches). Conjecturally it is a way to non-continuous travel in the KSBA compactification of the moduli space of surfaces of general type. It depends on a particular MMP. In that paper, we verified the conjecture in several cases, but many remain open. Beyond the certainty of the conjecture, it would be interesting to know about changes in the topology or differential structure after traveling through a wormhole. In this talk, I will exemplify what we know, and I will state open questions, which also include a mysterious combinatorial invariant delta that remains constant in this journey and seems to be part of some particular sequence of integers.