Independent Studies in Groups and Graph Limits

  • Instructor: Dr Miklos ABERT
  • Contact: abert dot miklos at renyi dot hu
  • Prerequisites: basic group theory, linear algebra, basic probability theory and graph theory
  • Text: class notes

Course description: Graph convergence is a recently emerging subject that has active connections to ergodic theory, group theory, geometry and percolation theory. In particular, the theory of sofic groups is related to sparse graph convergence in many ways. The group will understand the basic notions and theorems through a mixture of problem solving and lecturing and then will cover some fresh results, some of which are not yet published even on arXiv. The students will also be exposed to some open problems. The aim of the course is not to solve one of these problems (although, that would be very welcome, too), rather to get access to a real research experience on a student appropriate level. This mostly follows the REU tradition at the University of Chicago. Abert taught in that program for several years. By the end of the course the students will get involved in an active area of research and will individually write up a nice, short piece of math in a neat, readable form. This is an advanced course that will be quite challenging.


  • amenability,
  • Benjamini-Schramm convergence,
  • spectral theory of graphs and groups,
  • expander graphs,
  • ultralimits.