Return to Colloquia & Seminar listing
Contact structures and categorification of Temperley-Lieb at [2] = q + q^-1 = 0
(note the special time change: NOON)
Algebra & Discrete Mathematics| Speaker: | Kevin Walker, Station Q (Microsoft) |
| Location: | 1147 MSB |
| Start time: | Fri, Feb 12 2010, 12:10PM |
The classification of tight contact structures on 3-manifolds can be reduced to the study of the representation theory of certain combinatorially defined categories. The objects of these categories are collections of non-crossing arcs in a disk (equivalently, non-crossing partitions), and so they can be thought of as categorifications of the Temperley-Lieb category (with parameter q such that [2] = q+q^-1 = 0). These categories have a semi-triangulated structure, and they can be embedded in the derived category of the poset of non-decreasing maps from {1...m} to {1...n}. The construction of this embedding involves a "cube of resolutions" similar to the one featured in sl_2 Khovanov homology.
The talk will be combinatorial: No knowledge of contact structures on 3-manifolds will be required, and not much knowledge thereof will be imparted either.
(note the special time change: NOON, not 1pm)