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 14-16 c.t. in room B045.

Lecturers: Prof. Dr. Sebastian Hensel and Prof. Dr. Markus Heydenreich

Registration: 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.	He-Schramm 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