Conformal and discrete conformal geometry of surfaces
Student No.:50
Time:Mon/Wed 9:50-11:25, 2017-06-6, 2017-6-7~2017-07-31 (no lectures during June 12-16, July 10-14)
Instructor:Feng Luo  [Rutgers University]
Place:Lecture Hall, Floor 3, Jin Chun Yuan West Building
Starting Date:2017-6-6
Ending Date:2017-7-31





This is learning and research seminar on 2-dimensional conformal geometry and its discrete version. We will begin with a proof of the uniformization theorem for Riemann surfaces and develop the basic tools for conformal geometry. These include the extremal lengths, harmonic measures and Green’s functions. In the discrete part, we will introduce the work of He-Schramm on circle packing and their solution to the Koebe conjecture in the countable case. We will also discuss our recent work on discrete conformal geometry of polyhedral surfaces and its relationship to the Koebe conjecture and convex surfaces. The students are encouraged to give talks in the seminar.  





Complex analysis and basic algebraic topology





Ahlfors, L, conformal invariants


Goluzin, geometric theory of a complex variables


Schramm, Transboundary extremal length, Journal d’Analyse Mathématique, December 1995, Volume 66, Issue 1, pp 307–329


Jenkins, J., univalent functions and conformal mapping.