I will discuss work in progress with John Francis and
David Gepner that applies techniques from factorization homology
to prove analogs of the Hochschild-Kostant-Rosenberg theorem.
More explicitly, for a commutative algebra in characteristic
zero, we will express its $E_n$ Hochschild (co)homology in terms of
its commutative (co)tangent complex. Similar results are due to
Calaque-Willwacher and Toën, but our approach avoids formality.
I hope to emphasize connections with topological field theory.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/6356