We're just beginning Bott & Tu's book, so I've temporarily reopened the group to new members.
Are you interested in reviewing or rounding out your knowledge of graduate-level mathematics? The purpose of this group is to undertake a structured study regimen to that end. Personally, I want to review various subjects and fill in some significant gaps in my own background. Initially, the plan is to cover approximately the material relevant to a PhD general exam in mathematics at roughly the same level of detail -- give or take a few topics depending on the proclivities of the members (my own bias is toward differential geometry and algebraic topology). If there is interest, the group may branch out into more specialized or detailed studies down the road. The idea is to set out a specific plan of study and meet once every week or two (as scheduling permits). Hopefully, meeting as a group will motivate us to make steady progress and allow us to learn from one another (and meet some interesting people). The book "Analysis, Manifolds, and Physics" by Choquet-Bruhat gives a good sense of the topics I'd like to cover. Anyone is welcome; you need not be a student (I'm not one). However, I ask that you realistically assess your own background and your ability to commit to a long-term programme. Basically, if you would feel comfortable signing up for an MIT graduate course in Algebra, Differential Geometry, or Topology, then this group may be a good fit.