Analysis Student Seminar Spring 2020

During this seminar we will investigate Liouville Quantum Gravity in some depth.

This is a graduate student seminar, with talks given by graduate students participants. We all attempt together to understand the topic being discussed. Of course, people with any level of background are welcome, and everyone is especially encouraged to ask questions.

Main Sources

These are the main articles we’ll make use of this semester. Other potentially useful sources are listed below the schedule.


All meetings are held on Wednesdays at 4pm in the Math Tower, Room 5-127.

Reading sections in parentheses are optional, and we’ll likely exclude them unless we have spare time.

DateSpeakerTopicReading Sections
1/29/2020N/ATopic Proposals and IntroductionN/A
2/5/2020Timothy AllandA Crash Course on Probability, MartingalesProb1 1-5
2/12/2020Timothy AllandAn Introduction to MartingalesProb1 6-7
2/19/2020Matthew DannenbergBrownian Motion, Brownian Bridges, Gaussian Random VariablesProb6 2.2.1-2.2.2, Prob7
2/26/2020Jack BurkartThe Continuous Gaussian Free FieldLQG2 1.2-1.3,(1.4)
3/4/2020N/AGo to the Analysis Workshop at the Simons Center!N/A
3/11/2020Ying Hong ThamMarkov and Conformal Properties of the GFF, Circle Regularization, Thick PointsLQG2 1.5-1.8
3/18/2020N/ASpring BreakN/A
3/25/2020N/AIntroduction to Liouville Quantum Gravity in the $L^2$ PhaseLQG2 2-2.2
4/1/2020N/ATypical Points for the Liouville Measure, Random Surfaces and Conformal StructureLQG2 2.3,2.5-2.7

Potentially Useful Materials

A few of these resources we’ll work through in detail. The rest should be thought of as context for those interested or as reference documents containing proofs of certain results we’ll use along the way.

This course website from a 2017 MIT class taught by Scott Sheffield contains several really useful resources.


Gaussian Free Fields

Liouville Quantum Gravity

The Brownian Map