Geometric analysis reading group
Time, place and subjectsThe geometric analysis reading group will meet on Friday at 14:00--16:00 in room MaD 245.
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)
The second part of the reading materials will base on the following possible topics according to the interests of the audiences.
- 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)
- Uniformazation of metric surfaces (based on the recent work of Professor Kai Rajala, also Bonk-Kleiner, Heinonen-Sullivan)
of the branch set for quasiregular mappings/mappings of finite
distortion (Bonk-Heinonen, Heinonen-Rickman, Koskela-Maly, ... )
Geometric parametrization of metric spaces (Heinonen-Keith,
Heinonen-Rickman, Heinonen-Rajala-Pankka, Heinonen-Wu, Pankka-Rajala-Wu)
of proper, discrete, open mapping with compact branch set.
(Church-Hemmingsen, Martio-Rickman-Vaisala, Martio, Vuorinen)
- Quasiregular mappings with wild branch set. (Rickman, Heinonen-Rickman, Semmes, Pankka-Drasin)
- Iwaniec-Sverak Conjecture (Hencl-Rajala, Rajala, Hencl-Koskela, Heinonen-Koskela)
Fall 2015, Schedule, Part II (BLD parametrization of metric spaces)
- 24 Sep., Decide topitcs.
- 2 Oct., Metric orientation and Sobolev spaces, Ville Kirsilš.
- 9 Oct., Whitney forms and Stokes Cycle, Debanjan Nandi.
- 16 Oct, Proof of discreteness and openness, Changyu Guo.
- 23 Oct., Further discussions and open problems for paper I, Group discussion.
- 30 Oct., Geometric measure theory, Katrin Fšssler.
- 6 Nov., Section 5 Tangent Cone, Vellis Vyron.
- 13 Nov., Section 6 Tangent map, Zheng Zhu.
- 20 Nov., Section 7 Proof of existence, LudÍk Kleprlik
- 27 Nov., Section 8 Smoothability of Lipschitz manifolds, TBD
- 4 December, Further discussions and open problems for paper II, Group discussion.
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.
- 6 Feb, A short overview of problems related to the branch set of a discrete and open mapping, Decide topitcs.
- 13 Feb, On Newman's theorem for finite-to-one open mappings on manifolds, Changyu Guo.
- 20 Feb, The extension of interiority, with some applications, Aapo Kauranen.
- 27 Feb, Discrete open mappings on manifolds, Sebastiano Nicolussi Golo.
- 6 March, Minimal mappings in euclidean spaces, Tuomo Ojala.
- 13March, Local topological properties of countable mappings, Sita Benedict.
- 20 March, Measure properties of the branch set and its image of quasiregular mappings, Debanjan Nandi.
- 27 March, A note on proper maps, Nijjwal Karak.
- 3 April, Holiday, no meeting.
- 10 April, A capacity inequality for quasiregular mappings, Lizaveta Ihnatsyeva and Vyron Vellis.
- 17 April, Remarks on the Iwaniec-ŠverŠk conjecture, Ville Kirsila and Tuomo Akkinen.
- 24 April, Reshetnyak's theorem and the inner distortion, Lukas Maly.