This is a topics course in analysis and varies from year to year. It may be repeated for credit.
In Fall 2014, the topic is hyperbolic geometry. In the first half of the course, we will study the basics of 2- and 3-dimensional hyperbolic geometry: length, area, volume, and trigonometry. The second half of the course will focus on hyperbolic surfaces and 3-manifolds and techniques for computing their area or volume. Particular attention will be devoted to the connections between hyperbolic volume and knot theory, number theory and Lie theory. |