PC Seminar: A first passage metric of the Gaussian free field
- Date: 29 April 2025, 13:15–14:15
- Location: Ångström Laboratory, 64119 + Zoom
- Type: Seminar
- Lecturer: Lukas Schoug (KTH)
- Organiser: Matematiska institutionen
- Contact person: Sascha Troscheit
Lukas Schoug (KTH) gives this seminar. Please note unusual day and time. Welcome to join!
Abstract: Using the Gaussian free field (GFF) and its level sets, we construct a conformally invariant random metric on a planar domain, in which, heuristically, the length of a curve is given by the maximal value of the GFF on said curve. Aside from the interesting geometry of the metric, one motivation for its study is in the context of string theory: in the 1980s, Polyakov introduced Liouville quantum gravity (LQG) -- a one-parameter family of random surfaces -- with the goal of describing a conformally invariant string theory, however, LQG is conformally covariant instead. We conjecture that our constructed metric should arise as a renormalised limit of LQG and describe the model that Polyakov aimed to construct.
Participte on site or via Zoom link (meeting ID 65089679653).
This is a seminar in our seminar series on Probability and Combinatorics (PC).