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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Archived Curricula Guide 2016–2018
Curricula Guide is archieved. Please refer to current Curricula Guides
MATE5332 Introduction to conformal geometry and quasiconformal maps 10 ECTS
Organised by
Person in charge
Department of Mathematics and Statistics, Matti Vuorinen
Preceding studies
Measure theory, topology

Learning outcomes

The course provides a gateway to modern mapping theory.
After the course, the student will be able to read research papers and to start research in this topic.


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.

Teaching methods

Teaching method Contact Online
Lectures 56 h 0 h
Exercises 26 h 0 h

Not lectured 2014-2016.

Teaching language


Modes of study

Option 1
Available for:
  • Degree Programme Students
  • Other Students
  • Doctoral Students
  • Exchange Students
  • In English
Written exam
  • In English
Option 2
Available for:
  • Degree Programme Students
  • Other Students
  • Doctoral Students
  • Exchange Students
Written exam
  • In English


Numeric 0-5.

Belongs to following study modules

Department of Mathematics and Statistics
Archived Teaching Schedule. Please refer to current Teaching Shedule.
Implementation details are unavailable.
Department of Mathematics and Statistics
DP in Mathematics and Statistics
DP in Mathematics
DP in Statistics
MDP in Information Security and Cryptography
Finnish Study Modules