SUMMER SCHOOL
SLE, conformal welding, and random planar maps.

Stochastic Loewner evolution, Course notes 2006
by M. Zinsmeister
lecture notes.
Part 1
Contact Huy Tran for instructions
[presenter: Eveliina Peltola, Helsinki]

Stochastic Loewner evolution, Course notes 2006
by M. Zinsmeister
lecture notes.
Part 2
Contact Huy Tran for instructions
[presenter: Jianping Jiang, U Arizona]

Halfplane capacity and conformal radius
by S. Rohde, C. Wong
Proc. Amer. Math. Soc. 142 (2014), 931938
Prove the main theorem 1.2
[presenter: Angel Chavez, U Arizona]

Quasiconformal variation of slit domains
by C. Earle, A. Epstein
Proc. Amer. Math. Soc. 129 (2001), 33633372
Prove Theorem 1, and theorems 2 and 3 in the analytic case.
[presenter:Kirill Lazebnik, SUNY Stony Brook]

The Loewner equation and
Lipschitz graphs
by S. Rohde, H. Tran, M. Zinsmeister
preprint
The main theorem of the paper is Theorem 1.1. The presenter should
emphasize what conditions to get the existence of the curve.
[presenter: O"mer Faruk Tekin, UCLA ]

Spacefilling curves and phases of the Loewner
equation
by J. Lind, S. Rohde
Indiana Univ. Math. J. 61 (2012), 22312249
Prove the main theorem 1.1 (section 3.2) and elaborates theorem 1.3
(section 4) if time permits.
[presenter: JhihHuang Li, Geneva ]

Loewner curvature
by J. Lind, S. Rohde
preprint 2014
Do sections 2, 3, 4.1 and Theorem 5.1.
[presenter: Kyle Kinneberg, UCLA]

Backward SLE and the symmetry of welding
by S. Rohde, D. Zhan
arXiv:1307.2532
.
The main theorem is Theorem 1.1. The presenter may look at the authors'
slide at https://www.ipam.ucla.edu/publications/iagws4/iagws4_11254.pdf. Do
sections 2, 3, and 6.
[presenter: Ben Mackey, Michigan SU]

Random curves, scaling limits and
Loewner evolutions
by A. Kemppainen, S. Smirnov
arXiv:1212.6215
Prove the main theorem 1.3 (section 3). If time allows, discuss
applications to statistical physics models.
[presenter: Alexander Glazman, Geneva ]

Conformal welding and Koebe's theorem
by C. Bishop
Ann. of
Math. (2) 166 (2007), 613656
Do the introduction and prove Theorem 4 and possibly Theorem 2.
[presenter: Larissa Richards, Toronto]

Random confor
mal weldings
by K. Astala, P. Jones, A. Kupiainen, E. Saksman
Acta Math. 207 (2011), 203254
and :
Random curves by confor
mal welding
by K. Astala, P. Jones, A. Kupiainen, E. Saksman
C. R. Math. Acad. Sci. Paris 348 (2010),
257262.
The presenter should give an overview of the first paper (based on the
second). We care about the construction (section 3). Give an overview of
section 4 and do section 5.
[presenter: Miika Nikula, Helsinki]

Recurrence of distributional limits of finite planar graphs
by I. Benjamini, O. Schramm
Electron. J. Probab. 6 (2001), 13 pp.
Prove the main theorem in the triangulation case (Proposition 2.1). Discuss
the ring lemma and skip the proof of lemma 2.3. The presenter can mention a
quantitative version of lemma 2.3 in the paper of GurelGurevich and
Nachmias
[presenter: Gerandy Brito, U Washington]

Uniform infinite planar triangulations
by O. Angel and O. Schramm
Comm. Math. Phys. 241 (2003), 191213
Main parts to present are Sections 3 and 4.
[presenter: Krystal Taylor, IMA]

On the Riemann surface type of random
planar maps
J.T. Gill, S. Rohde
Rev. Mat. Iberoam. 29 (2013), 10711090
Do the proof of Theorem 1.1 and application to UIPT.
[presenter: Joe Adams, SUNY Stony Brook]

Recurrence of planar graph
limits
O. GurelGurevich, A. Nachmias,
Ann. of Math. (2) 177 (2013), 761781
We are interested in the recurrence of random walk in UIPT. Do sections 3,
4 and 5 (rough).
[presenter: Martin Tassy, Brown]

SLE Coordinate
Changes
O. Schramm, D. Wilson,
New York J. Math. 11 (2005), pages 659 to 669
Define SLE(kappa, roh) and prove Theorem 3 for
the case m=1.
Also do Theorem 4.6 in Section 4 of Rohde and Zhang's paper.
[presenter: Laurie Field, U Chicago]

Liouville quantum gravity and KPZ formula
B. Duplantier, S. Sheffield,
Invent Math (2011), 333393
Show Proposition 1.1 which makes sense of random measure
mu = exp(gamma*h) where h is a Gaussian Free Field. This random
measure is related to the boundary measure constructed in
Kari Astala, Peter Jones, A. Kupianinen, Eero Saksman's paper.
(That boundary measure is constructed
from the trace of Gaussian Free Field to the boundary).
[presenter: Zhiqiang Li, UCLA]