The Erlangen program of F.Klein (influenced by S.Lie) defines geometry as a study of invariants under a certain group action. This approach proved to be fruitful much beyond the traditional geometry. For example, special relativity is the study of invariants of Minkowski space-time under the Lorentz group action. Another example is complex analysis as study of objects invariant under the conformal maps.
In this course we consider in details SL(2,R) group and corresponding geometrical and analytical invariants with their interrelations. The course has a multi-subject nature touching algebra, geometry and analysis.
There are no prerequisites beyond a standard undergraduate curriculum: elements of group theory, linear algebra, real and complex analysis. Some knowledge of Lie groups and Hilbert spaces would be helpful but is not obligatory.
Lectures will demonstrate numerous connections between various areas of mathematics. Therefore the course will benefit students wishing to see their research field in a broader context.
The best approximation to the Lecture Notes at the moment is my paper 'Erlangen Program at Large: Outline', see "Course Materials" section and the Bibliography. This will be significantly edited and expanded during the semester.
There are no prerequisites beyond a standard undergraduate curriculum: elements of group theory, linear algebra, real and complex analysis.
Some knowledge of Lie groups and Hilbert spaces would be helpful but is not obligatory.