The String Coffee Table

Streetfest Workshop I

Posted by Guest

Greetings from Canberra!

It is very pleasant here. There was a good frost this morning and some black swans with their chicks down by the lake. Most of the Streetfest participants moved down here yesterday in buses or cars or planes, mostly uneventfully, although Tim Porter found himself driving on a dirt road through the mountains after realising that the main highway south actually went to Melbourne. The workshop started this morning. We’re so busy that there’s almost no time to tell you what’s going on.

Kapranov was up first: the prequel to last week’s talk on NC Fourier transforms. At the end there was a little discussion with some people wondering exactly how this connects to Connes’ NCG.

Panov spoke about model cats, homotopy colimits and toric topology. Toric topology is the study of torus actions on manifolds or complexes with a rich combinatorial structure in the orbit quotient. First he defined ‘face rings’ which are Stanley-Reisner algebras of simplicial complexes. Ross Street later highly recommended Stanley’s revolutionising of combinatorics … something I must look into later. The Poincare series for $R [ K ]$ was defined, and Panov listed some problems that could be attacked with this machinery: the Charney-Davis conjecture, the question of when $\mathrm{Ext}_{k [K]} (k,k)$ has rational Poincare series, and something called the g-conjecture - whatever that is.

Then he defined the David-Januszkiewicz space $DJ(K)$, which seems to be important because it turns up in a theorem (Panov, Ray, Vogt) giving a homotopy commutative diagram involving the loop functor $\Omega: \mathbf{Top} \rightarrow \mathbf{TMon}$ into the monoid category.

Marni