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Is there a central wiki or something where open questions (and relevant research on them) takes place?

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Going by the title of your question if you are trying to find out the "Best place to find... latest Research" I think I would go by http://arxiv.org. Lots of papers out there. Many papers are junk (including some of mine... hehe) But you can also find papers on open problems by serious mathematicians.

For me, reading papers from arxiv and trying to understand them has helped me a lot to learn new stuff.

For a wiki like site, you might check, http://garden.irmacs.sfu.ca/

For collaborative mathematics: You might also do google search on the polymath project which started from this blog post: http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/

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