Matt Might does excellent academic blogging. So does RJ Lipton and, to some extent, Terence Tao (although his is for a specialist audience). I would advise wri

Matt Might does excellent academic blogging. So does RJ Lipton and, to some extent, Terence Tao (although his is for a specialist audience). I would advise writing, writing, writing. I wouldn't worry too much about #1; a cohesive set of explanatory references and definitions goes a long way. For #2 - I would actually suggest for #2 to focus on "explaining the papers you work through for seminars". I.e., do a public expository discussion similar to the "Present a Paper" internal seminars labs often old. Practitioners often don't get access to papers in a fresh way.