Fuchsian groups are discrete groups of rigid motions of the hyperbolic plane through which the topological, geometric and analytic properties of hyperbolic surfaces (known as 2-dimensional manifolds) can be studied. Here we will introduce these beautiful ideas and explore their connections with other areas of mathematics including complex analysis, theory of Riemann surfaces, number theory, Lie groups, differential geometry, and the topology and geometry of 3-manifolds. Evaluation will be based primarily on projects, homework assignments, and exams.

Prerequisites: Mathematics 301 or 305, and Mathematics 312 or 315, or permission of the instructor. No enrollment limit (expected: 15).

Hour: SUSSKIND