## Talk page

Title:

Permutations in random geometry - Lecture 2

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Abstract:

andom permutons, called the skew Brownian permutons, describing the scaling limit of various natural models of random constrained permutations. After that, the main goal will be to discuss some connections between random permutations and random geometry. In particular, we will focus on the problem of the longest increasing subsequence in permutations sampled from the skew Brownian permuton and its connection with the study of certain directed metrics on planar maps, which conjecturally should converge in the limit to a notion of "directed Liouville quantum gravity metric.

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