The n-Category Café

Close to my heart today was the talk by Greg Moore on his work with Jacques Distler and Dan Freed (which we have talked about before here on various occasions) on the differential cohomology of orientifold backgrounds for string sigma-models.

The slides he pesented are available here:

• Greg Moore, The RR-charge of an orientifold.

Yesterday Alexander Kahle told us about his work with Alessandro Valentino on refining the aspect of T-duality that is known as topological T-duality from an operation acting on just K-theory cocycles to an action on differential K-classes – the RR-fields:

• Alexander Kahle, Alessandro Valentino, T-duality and Differential K-Theory .

Not that I necessarily have to travel to hear about this, but Arthur Bartels gave another nice summary of the main result of

• Arthur Bartels, Chris Douglas, André Henriques, Conformal nets and local field theory

on the symmetric monoidal tricategory of conformal nets.

Chris Woodward talked about his joint work with Kathrin Wehrheim on Lagrangian correspondences and $A_\infty$-category valued TFTs.

A bunch of us (Samson Abramsky, Peter Hines, Lou Kaufman, Sanjeevi Krishnan, Jimie Lawson, Gordon Plotkin, Jamie Vicary, …) are also in Germany, at Oberwolfach’s CS-counterpart Dagstuhl where The Semantics of Information organized by Mike Mislove and Keye Martin is taking place.

Hisham Sati gave a brief survey of aspects of Geometric and topological structures related to M-branes.

Yan Soibelman talked about his work with Maxim Kontsevich on motivic Donaldson-Thomas invariants (see there for a review).

Maybe I find time to post my notes later. But we were told tat just a few minutes before the talk, Maxim Kontsevich submitted a preprint with more details to the arXiv. So I suppose tomorrow I can to that, too.

By the way, a message to my fellow $n$-lab assistants: i haven’t been able to open the $n$-Forum page for days (I think precisely for the days that I am here in Oberwolfach): when I point my browser to it, it keeps loading and loading and loading, and nothing ever appears. So that’s why I haven’t been logging my recent edits.

Ezra Getzler gave again a talk on his work on the topology of the moduli space of punctured surfaces. By putting a filtration on this that reflects the $n$-categorical filtration of the modular operad, one can very efficiently read off various kinds of classication results of 2d TQFTs from the homotopy groups of the filtered subspaces.

I put my notes from his talk at 2d TQFT into the section Filtrations of the moduli space of surfaces.

Alexei Davydov spoke about how two vertex operator algebras may appear as the left and right chiral parts of a full 2d CFT precisely if their modular tensor categories of representations have the same Witt class.

Notes on the central statement I put into the section Full versus chiral CFT at conformal field theory.

I missed the reference to be given here, will try to provide it later.

Kentaro Hori gave a review of the path-integral heuristic argument for seeing T-duality for the string on the circle. So I used the opportunity to add that part of the standard story to the $n$Lab entry, at Path integral heuristics deriving T-duality.

If I understand correctly then Kentaro Hori’s point is to give a particularly elegant collection of auxiliary fields on the worldsheet such that T-duality becomes manifest simply by integrating these out in two different orders.

He also did the superstring analog, but that I found too tedious to type out.