Just gave my talk, and chatted to Nathan Geer and a few other people afterwards, which was nice! A few months ago I met Nathan over the internet when I discovered that his math work intersects mine – his interests include quantum (super)algebras and low dimensional topology and his website is http://www.math.gatech.edu/~geer/. His work looks impressive. One of the things he and another guy have done is define a link invariant using sl(2,1) that is basically the quantum link invariant from quantum sl(2,1) multiplied by some constant. The usual Reshetikhin link invariant coming from quantum sl(2,1) is zero as the quantum superdimensions of the relevant representations are zero. However, they found a way around this.
In my talk I could only skim over the results in my PhD thesis – if you´d like more detail about them then please download my thesis which is on the arxiv at http://lanl.arxiv.org/abs/math.QA/0601170 . All details are in the thesis, and some (eg about the Birman-Wenzl-Murakami algebra) are explained in more detail in my most recent paper that can be downloaded from the arxiv at http://lanl.arxiv.org/abs/math.QA/0607049 .
The conference has 6 more days to run – there have been some very impressive, understandable and interesting talks. Sir John Ball, the opening speaker in the opening ceremony, mentioned how important it was for mathematicians to be involved with dealing with the big issues of society (eg global climate change) which I agree with. We can´t think of ourselves as divorced from society. Coming to this conference was a good decision.
Highlights for me have been –
Avi Wigderson´s (http://www.math.ias.edu/~avi/ ) talk – P, NP and mathematics – a computational complexity perspective,
Etienne Ghys´(http://www.umpa.ens-lyon.fr/~ghys/ ) talk – Knots and dynamics
These guys are both very good speakers – I wholeheartedly recommend going to any of their future talks.
Troy´s enjoyed Madrid – apart from the opening ceremony and my talk he´s been enjoying the Madrid sun, boulevards, and shopping, especially Burberry!