Geometric analysis reading group
Time, place and subjects
The geometric analysis reading group will meet on Friday at 14:0016:00 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 (quasilight, 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. For which classes of mappings, the branch set is empty (including the wellknown Martio's conjecture) (Based on the work of Martio, HeinonenBonk, HeinonenKilpelainen, OnninenKovalev, RajalaOnninenKovalev)
 Uniformazation of metric surfaces (based on the recent work of Professor Kai Rajala, also BonkKleiner, HeinonenSullivan)
 Size
of the branch set for quasiregular mappings/mappings of finite
distortion (BonkHeinonen, HeinonenRickman, KoskelaMaly, ... )

Geometric parametrization of metric spaces (HeinonenKeith,
HeinonenRickman, HeinonenRajalaPankka, HeinonenWu, PankkaRajalaWu)
 Rigidity
of proper, discrete, open mapping with compact branch set.
(ChurchHemmingsen, MartioRickmanVaisala, Martio, Vuorinen)
 Quasiregular mappings with wild branch set. (Rickman, HeinonenRickman, Semmes, PankkaDrasin)
 IwaniecSverak Conjecture (HenclRajala, Rajala, HenclKoskela, HeinonenKoskela)
Fall 2015, Schedule, Part II (BLD parametrization of metric spaces)
 24 Sep., Decide topitcs.
 2 Oct., Metric orientation and Sobolev spaces, Ville Kirsilä.
 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 Fässler.
 6 Nov., Section 5 Tangent Cone, Vellis Vyron.
 13 Nov., Section 6 Tangent map, Zheng Zhu.
 20 Nov., Section 7 Proof of existence, Ludêk 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 finitetoone 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 IwaniecŠverák conjecture, Ville Kirsila and Tuomo Akkinen.
 24 April, Reshetnyak's theorem and the inner distortion, Lukas Maly.