- What (sub)field does this research fall under? What is the general context of this research? If it makes connections to areas outside of this field, what are they and how are they connected?
- What are the major theorems/results? When possible, include a small example to illustrate. What are the authors' favorite examples?
- If they make a point of it, what are the authors' favorite tools for proving their results or doing calculations?
- Why is this paper of interest to the general mathematical community? Why is it of interest to you?

- Is there anything about the style of the writing (examples, formatting, etc.) that made this paper particularly easy or difficult to read?
- Who are the authors? For example, can you find out, when they wrote the paper, what stage of their career were they in? Were they professors? researchers from industry? Where are they based right now? If possible, provide links to their webpages.
- How/where did you find the paper? If you got it from ArXiV, has it been accepted by a major journal (i.e. peer reviewed) yet?
- If you work with any of your classmates reading through the same paper, include that information.

A reasonable place to start is in a paper's abstract. But document of yours should read more like an *extended* abstract, and include specific references to theorem numbering etc. On your first pass through, skip any sections titled "preliminaries". If you need help getting started or processing definitions, you're welcome to come ask for help. But, in general, it's ok to focus on what nouns and adjectives are important to the paper without fully processing what those nouns and adjectives mean.

- The ArXiV, especially group theory, representation theory, and rings and algebras, though relevant papers also show up in other sections like combinatorics and quantum algebras.

- MathSciNet: access this while you're on campus (it's behind a pay wall, but CUNY has a campus-wide license). You can search by MSC code (Mathematics Subject Classification), like 20K01 for "Finite abelian groups" or 05E18 for "Group actions on combinatorial structures". If you try to find a paper via "Find it!" and can't, check the ArXiV or the authors' websites.

- Of course, there's good old fashioned flipping through journals. Advances, Annals, Inventiones, and Crell are some of math's top-ranked general journals, and Journal of Algebra is the top-ranked journal dedicated specifically to algebra. Each of the major societies, like AMS, LMS, AustMS, etc., have multiple important journals. A relatively complete list of mathematical journals, with their rankings according to AustMS, is here. Again, many of the papers published in these journals are behind pay walls, so either download the PDFs while you're on campus, or look for versions elsewhere once you've found something you want to read.
- Go to talks, and look up related publications. City's weekly colloquium is on Thursdays. There are also several relevant seminars going on down at the Graduate Center.