Uusi opinto-opas (sisältäen myös opetusohjelmat) lukuvuodelle 2018-2019 sijaitsee osoitteessa https://opas.peppi.utu.fi . Tältä sivustolta löytyvät enää vanhat opinto-oppaat ja opetusohjelmat.

The new study guide (incl. teaching schedules) for academic year 2018-2019 can be found at https://studyguide.utu.fi. This site contains only previous years' guides.

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Arkistoitu opetusohjelma 2014–2015
Selaat vanhentunutta opetusohjelmaa. Voimassa olevan opetusohjelman löydät täältä.
MATE5332 Introduction to Conformal Geometry and Quasiconformal maps 5–10 ECTS
Period I Period II Period III Period IV
Language of instruction
Type or level of studies
Advanced studies
Course unit descriptions in the curriculum
Matematiikan tutkinto-ohjelma (FM)
Department of Mathematics and Statistics

General description

Euclidean geometry studies configurations of points such as triangles and polygons and those properties of these
that are invariant under similarity transformations. Hyperbolic geometry is largely analogous to the Euclidean geometry, but a key feature now is invariance with respect to conformal automorphisms of the unit disk, Möbius transformations. Conformal geometry refers to generalization of these notions to subdomains of higher dimensional Euclidean spaces. These ideas are then applied to study familiar classes of maps such as bilipschitz maps and their generalizations, quasiconformal maps. The goal is to develop modern mapping theory in this framework. Some of the key tools, such as the extremal length of a curve family, are based on measure theory.

The course consists of weekly exercises in a group.

Teacher responsible

Matti Vuorinen


10-Mar-2015 – 12-May-2015
Independent work
Tue 10-Mar-2015 - 12-May-2015 weekly at 12-14, The time and place will be updated here during the week 10.

Further information

The information regarding the course schedule will be updated here during the week 10.