Topics in Geometric Topology

We will mainly discuss the following content in this semester.

Part 1. Basic framework in analysis on metric spaces. We will cover topics such as covering lemmas, fractal dimensions, modulus, quasiconformal mapping, quasisymmetry, Loewner spaces, Poincare inequality, conformal dimension, etc.

Part2. Application of techniques of analysis on metric spaces into geometric group theory. We will cover topics such as hyperbolic groups, the boundary at infinity, visual metric, Gromov Hausdorff convergence, weak tangents, Cannon conjecture, Kapovich-Kleiner conjecture, etc.

If time permits, we may cover more subjects in related areas.

A student in this course will be assigned a grade based on a presentation on a topic related to analysis on metric space. The student can choose the direction that best suits his/her interests. A more ambitious student can consider a subsequent research project on the same topic.

This semester, the course is taught in English as part of a courses-taught-in-English program in PKU. The presentations will be in English as well.

Time: Monday 1:00pm-3:00pm(odd weeks)

          Wednesday 10:00am-12:00am(all weeks)

Location: Teaching Building No. 1, Classroom 304.

Preliminaries: Real Analysis. Some knowledge of complex analysis is very helpful but not essential.