baez videos on geometric representation theory

john baez is publishing on the web an amazing set of video lectures for his quantum gravity seminar on geometric representation theory — which aims to understand groups representations (as linear operators on vector spaces) from the viewpoint of more standard ideas about group actions. since quantum mechanics essentially studies symmetries on hilbert spaces (via group representations), this approach can evidently help us understand quantum physics from the more classical ideas we’re already familiar with.

to see the videos and lecture notes, go here.

since i’m not sure i’ve ever explicitly written about john baez here — well, he’s essentially my favorite living mathematician; he’s a mathematical physicist (and mit alumnus) who uses higher-dimensional algebra and category theory to study theoretical physics (titillating my obsession with “mathematical structure” and its shocking correspondence with “physical reality”), who takes a serious interest in publicly writing about his work, and who does so with unparalleled lucidity. even if you don’t know much mathematics, i encourage you to watch the first video lecture — if not to glimpse how a mathematician thinks or to get some vague idea about the kind of mathematics i enjoy, just for the hell of it.

if you’re still bored or want to have a better idea what baez is talking about, alistair savage has some great slides on “geometric methods in representation theory” here. they’re aimed at a general audience, but don’t offer too much information (being slides).