Student Seminar
Circle packings and random walks
Winter semester 2021/2022
This seminar focusses on the connection of circle packings and random walks, and a recently established connection between these two objects. Central part of the seminar are the interplay between geometric and probabilistic objects. We cover the theory of random walkson graphs and its connection with electric network theory; the circle packing theorem; parabolic and hyperbolic packings; planar local graph limits; uniform spanning trees of planar graphs.
Target group: Master students in Mathematics. Bachelor students with strong background in geometric group theory or discrete probability theory and keen interest in the topic may apply for admission.
Literature (preliminary):
 Asaf Nachmias: Planar Maps, Random Walks and Circle Packing
Lecture Notes in Mathematics 2243, Springer Open, 2020  Kenneth Stephenson: Introduction to Circle Packing.
Cambridge University Press, 2005.  Geoffrey Grimmett: Probability on Graphs.
Second edition, Cambridge University Press, 2018.
Time: Thursday 1416 c.t. in room B045.
Lecturers: Prof. Dr. Sebastian Hensel and Prof. Dr. Markus HeydenreichRegistration: Interested students please (pre)register by email to Prof. Hensel.
Planned schedule (subject to change):
Date

Speaker  Topic 
28 Oct 
S.H. 
Recap: Hyperbolic geometry 
4 Nov 
A.R.P. 
Circle packings I 
11 Nov 
S. 
Circle packings II 
18 Nov 
E.H. 
Random walk and electrical network I 
25 Nov 
L.B. 
Random walk and electrical network II 
2 Dec 
A.W. 
HeSchramm Theorem 
9 Dec 
M.H. 
Planar local graph limits 
16 Dec 
A.W. 
Recurrence of random planar maps 
13 Jan 
P.P. 
Uniform infinite planar triangulation/quadrangulation 
20 Jan 
D.S. 
Uniform spanning trees and planar graphs I 
27 Jan 
A.C. 
Uniform spanning trees and planar graphs II 