Two Flavours of Random Geometry: Geodesics in the Directed Landscape and Liouville Quantum Gravity
Name
bhatia-mananb-phd-math-2026-thesis.pdf
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7.91 MB
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49645309b0eff324a9b77825791955c7
Author(s)
Bhatia, Manan
Advisor(s)
Sheffield, Scott
Date Issued
May 2026
Publisher
Massachusetts Institute of Technology
Abstract
In recent years, random geometry has developed into a subject in its own right, with the directed landscape and Liouville quantum gravity serving as central examples. Despite their very different origins, these models share striking similarities, particularly in their coalescent geodesic geometry. In this thesis, we discuss a collection of works motivated by viewing these models through a common lens, highlighting the transfer of ideas and techniques between the two settings.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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