Continuity in $\kappa$ of Welding Homeomorphism of SLE$_\kappa$.
Atul Shekhar (TIFR-CAM)
| Speaker |
Atul Shekhar (TIFR-CAM)
|
|---|---|
| When |
Feb 22, 2022
from 04:00 PM to 05:00 PM |
| Where | zoom colloquium |
| Contact Name | Pramila |
| Contact Phone | 08066953702 |
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Abstract: The welding homeomorphism of a Jordan curve (or an arc) is a gluing rule which preserves the conformal structure of the inside and the outside of the curve. We will consider the welding homeomorphism of SLE$_\kappa$ and prove that these homeomorphisms are continuous in the $\kappa$ parameter for $\kappa \in [0,4]$. Our motivation is to study the continuity in $\kappa$ of SLE itself. We will also draw several parallels of this with the Liouville quantum gravity. This is based on a joint work with Dmitry Belyaev and Vlad Margarint.