Lectures:  Thursday from 3:30 to 4:45 and Friday from 10:30 to 11:45 
Classroom:  Lecture Hall 6 
Instructor:  Priyavrat Deshpande. 
Contact:  Office: 403 

phone: 962  
email: pdeshpande AT cmi DOT ac DOT in  
Office
Hours: 
Thursdays from 2:00 to 3:00
p.m. 
Texts:  Useful reading material (in alphabetical order):

Prerequisites: 
Linear algebra, finite
groups, LaTeX proficiency, and/or permission from the
faculty advisor. 
Grading:  The homework will be assigned roughly every 2 weeks. Each
student will have to do a project. This includes a report
(prepared in LaTeX) and a 40 minutes boardtalk.

Web:  http://www.cmi.ac.in/~pdeshpande/reflections.html 
Discrete isometry groups of more general Riemannian manifolds generated by reflections are also interesting. The most important class arises from Riemannian symmetric spaces of rank 1: the nsphere (finite reflection groups), the Euclidean space (corresponding to affine reflection groups), and the hyperbolic space (hyperbolic reflection groups).
Coxeter groups grew out of the study of reflection groups. A reflection group is a subgroup of a linear group generated by reflections while a Coxeter group is an abstract group generated by involutions (i.e. reflections), and whose relations have a certain form (corresponding to hyperplanes meeting at a nonobtuse angle). All finitely generated reflection groups are Coxeter groups and vice versa. We will explore how the geometry and topology of reflection groups helps us understand their group theoretic properties.
A project should consist of a short introduction to a topic (or a
survey) or proof of a result and its implications. For example, a
project on Artin groups may include their definition, examples,
basic properties and statements of (some of the) important results
etc. On the other hand a project on the three reflections theorem
should include a detailed proof and its implications.
Students are welcome to choose topics on their own (even outside
the above list). A topic should be finalized before the end of
January. The final report (68 pages) is due in the last week of
March. Presentations will be scheduled during the month of April.
It is students' responsibility to keep the instructor updated
regarding the project work.