Geometric analysis reading group    

Back to homepage

Time, place and subjects

The geometric analysis reading group will meet on Friday at 14:00--16:00 in room MaD 245.  

In the first part of the reading group, we focus on basic properties of discrete and open mappings between topological/generalized manifolds. In particular, we study together some old papers on various properties of topological (quasi-light, discrete, open, monotone, ...) mappings between manifolds.  The central aim is to get familiar with the "branch set" of a topological (in particular discrete and open) mapping.

The second part of the reading materials will base on the following possible topics according to the interests of the audiences.
  1. For which classes of mappings, the branch set is empty (including the well-known Martio's conjecture) (Based on the work of Martio, Heinonen-Bonk, Heinonen-Kilpelainen, Onninen-Kovalev, Rajala-Onninen-Kovalev) 
  2. Uniformazation of metric surfaces (based on the recent work of Professor Kai Rajala, also Bonk-Kleiner, Heinonen-Sullivan)
  3. Size of the branch set for quasiregular mappings/mappings of finite distortion (Bonk-Heinonen, Heinonen-Rickman, Koskela-Maly, ... )
  4. Geometric parametrization of metric spaces (Heinonen-Keith, Heinonen-Rickman, Heinonen-Rajala-Pankka, Heinonen-Wu, Pankka-Rajala-Wu)
  5. Rigidity of proper, discrete, open mapping with compact branch set. (Church-Hemmingsen, Martio-Rickman-Vaisala, Martio, Vuorinen)
  6. Quasiregular mappings with wild branch set. (Rickman, Heinonen-Rickman, Semmes, Pankka-Drasin)
  7. Iwaniec-Sverak Conjecture (Hencl-Rajala, Rajala, Hencl-Koskela, Heinonen-Koskela)

Fall 2015, Schedule, Part II  (BLD parametrization of metric spaces)

Spring 2015, Schedule, Part I (Gneral properties of branched covering)

Orders of topics might change and some papers are relatively longer and we could split it into two times.