Reading Seminars on LQG and Related Topics
The purpose of this semester-long seminar is to study constructions and basic facts around Liouville quantum gravity. It will also cover the general theory of Gaussian free field Schramm–Loewner Evolution and random planar maps. Several more in-depth topics may be included depending on circumstances.
Time: Every Thursday 1-3 pm.
Location: Room 1513.
Tencent Meeting ID: 368 4116 5493.
Talk Schedule (tentative)
9.30: Yuyang Feng - An overview of LQG theory and recent progresses based on [Gwy].
10.14: Gefei Cai - A brief introduction to the contents of the main material [BP].
10.21: Peng Yang - Section 1.1-1.4 of [BP]. Discrete GFF Dirichlet GFF defined via green function integration by parts.
10.28: Yutao Liang - Section 1.5-1.8 of [BP]. Reminders of functions spaces Dirichlet GFF defined as random distribution.
11.4: Hang Du - Section 1.9-1.12 of [BP]. Markov property conformal invariance circle average dimension of thick points.
11.11: Yuyang Feng - Section 2.1-2.4 of [BP]. Introduction to LQG construction of Liouville measure in the L2 phase γ-thick point as Liouville typical point.
11.18: Yu Liu - Section 2.5-2.8 of [BP]. Construction of Liouville measure in the L1 phase conformal covariance definition of random surfaces.
11.25: Everyone - Discuss exercises of GFF from section 1.13 of [BP] and problem list written by Gwynne.
12.2: Aoteng Xia - Section 3.12-3.15 of [BP]. The KPZ relation.
12.9: Everyone - Discuss exercises of LQG.
12.16: Midterm break. Read the article about SLE written by Gefei Cai.
12.23: Peng Yang - Section 1-4 of [Mil]. Reminders of complex analysis. [Law] as supplementary.
12.30: Yutao Liang - Section 5-8 of [Mil]. Reminders of stochastic calculus. [Law] as supplementary.
1.6: Yu Liu - Section 9 of [Mil]. Phases of SLE.
1.13: Hang Du - Section 10 of [Mil]. SLE6. Chapter 13 of [BN] as supplementary.
1.20: Yuyang Feng - Section 11 of [Mil]. SLE8/3. Chapter 14 of [BN] as supplementary.
1.27: Shengjing Xu (online) - Section 12-13 of [Mil]. SLE4. Chapter 15 of [BN]. SLE4.
2.3: Shuyuan Luo (online) - Section 4.1-4.4 of [BP]. Conjectures between random planar map and LQG Mullin-Bernard-Sheffield’s bijection LERW exponents.
2.10: Yuxuan Ge (online) - Section 5.1-5.3 of [BP]. The Neumann boundary GFF.
2.17: Guangyi Zou (online) - Section 5.4-5.7 of [BP]. The whole-plane GFF Dirichlet-Neumann GFF semi-circle averages quantum wedges. Chapter 3-4 in [DMS] as supplementary.
2.24: Everyone - Discuss exercises from section 5.8 of [BP] and problem list written by Gwynne.
3.3: Gefei Cai - Special lectures. Imaginary geometry (TBA).
3.10: Final exam week. Film screening.
References
[Gwy] E. Gwynne Random surfaces and Liouville quantum gravity Notices Amer. Math. Soc. 67 (2020) 484–491.
[BP] N. Berestycki and E. Powell Gaussian free field Liouville quantum gravity and Gaussian multiplicative chaos.
[WP] W. Werner and E. Powell Lecture notes on the Gaussian Free Field.
[Mil] J. Miller Schramm-Loewner Evolutions.
[Law] G. F. Lawler Schramm-Loewner Evolutions.
[BN] N. Berestycki and J. R. Norris Lectures on Schramm–Loewner Evolution.
[DMS] B. Duplantier and J. Miller and S. Sheffield Liouville quantum gravity as a mating of trees.