**Course:** Math 598: Mapping class groups and Teichmüller theory

**Time:** TTh 10:30--11:50am (tentative---we'll change the time after the first class meeting to suit everyone, if necessary)

**Instructor:** Chris Leininger

**Phone:** 265-6763

**Email:** clein (at) math.uiuc.edu

**Office:** 324 Illini Hall

**Text:** There is no required text for this course.

**Course Description** Teichmüller theory and mapping class
groups lie at the cross-roads of many fields of mathematics: low
dimensional topology, geometric group theory, complex analysis,
algebraic geometry, and dynamics. In this mini-course we'll survey
a number of results and techniques in the subject, covering as many
of the following topics as possible. If there is overwhelming interest, we may also choose to focus on one particular topic.

-simple closed curves, Dehn twists and finite generation

-hyperbolic, complex, and conformal structures

-measured laminations and foliations, Thurston theory

-quasi-conformal mappings and Ahlfors--Bers theory

-quadratic differentials, Teichmüller metric, affine groups

*HERE* is a brief description of what it looks like we'll end up doing... a syllabus if you will.

Don't forget, no class Thursday 3/16. We'll make it up somehow.

Here's the handout from class on Thursday 3/30 on the minimal area hyperbolic 2-orbifold.

**Logistics:** This mini-course is being offered during the second half of the semester, and will count as 2 credit hours. It can be
taken in conjuction with any of the other mini-courses being offered (which could be helpful in maintaining sufficent enrollment status) or can be can be taken by itself---the other mini-courses are NOT prerequisites. Lectures will begin March 6.

Other mini-courses offered Spring 2006:

-Session 1 (1/17--3/3): Igor Mineyev, ``Relative hyperbolicity''; Ely Kerman, ``Symplectic topology''; Robert Muncaster, ``Evolutionary game
theory'';

-Session 2 (3/6--5/3): Christian Haesemeyer ``Cohomology theories for algebraic varieties''