Cornell Math - MATH 751, Fall 2004

MATH 751: Berstein Seminar in Topology: Modern Methods in Geometry (Fall 2004)

Instructor: Kevin Wortman

Meeting Time & Room

The purpose of this course is to expose simple and powerful tools for use in research. In an effort to see as many ideas as the semester will allow, we will move rapidly between varied topics by harvesting the most digestible aspects of the literature. The emphasis will be placed on learning key principles from proofs that can be applied to future research problems.

Research interests of the individual students in attendance will determine the particular topics covered, although all topics will be extremely useful for any geometer to know. Examples could include: Mostow rigidity, laminations on surfaces, R-trees, quasi-isometries of lattices, ping pong, property (T), boundaries of groups, Gromov-Hausdorff space, Margulis' finiteness theorem, the thick-thin decomposition for hyperbolic manifolds, Gromov's polynomial growth theorem, contact structures, 3-dimensional geometries, a user's guide to ergodic theory, nonpositive curvature, basics from symmetric spaces, buildings, quasi-actions on trees, and measure equivalence.