Categorification on Broadway

Graduate Student Workshop

Organizing committee: S.Cautis, M. Khovanov, A.D. Lauda

Columbia, Dec 14-15, 2010

Mathematics Building, Room 528

ABOUT:

A short workshop on categorification.

The workshop is sponsored by the NSF and Columbia Math Department.

SPEAKERS:

Ben Elias (Columbia)
Anthony Licata (Stanford)

Daniel Murfet (UCLA)
Joshua Sussan (Max Planck)

SCHEDULE:

Tuesday, December 14th

10-11 am Ben Elias
11 - 11.15 amCoffee break
11.15 - 12.15 pm Anthony Licata
12.15 - 1.30 pm Lunch
1.30 - 2.30 pm Daniel Murfet

Wednesday, December 15th

10-11 am Ben Elias
11 - 11.15 amCoffee break
11.15 - 12.15 pm Anthony Licata
12.15 - 1.30 pm Lunch
1.30 - 2.30 pm Joshua Sussan
3 - 4 pm Ben Elias

TALKS:

  1. Daniel Murfet: Residues and matrix factorizations

    Abstract:
    I will describe joint work with Nils Carqueville and Toby Dyckerhoff relating the classical theory of residue symbols to homotopy categories of matrix factorizations.

  2. Anthony Licata:
    Part 1: Hyperplane arrangements, Hypertoric varieties, and Koszul Algebras: Combinatorics and Algebra
    Part 2: Hyperplane arrangements, Hypertoric varieties, and Koszul Algebras: Geometry

    Abstract:
    These talks will be an introduction to a family of Koszul algebras which are closely related to the combinatorics of hyperplane arrangements and to the geometry of hypertoric varieties. (Joint with Tom Braden, Nick Proudfoot, and Ben Webster)

  3. Joshua Sussan: Categorifications of the Jones-Wenzl Projector

    Abstract:
    The Jones-Wenzl projector is an important ingredient in the definition of the colored Jones polynomial and other topological invariants. We discuss a Lie theoretic categorification of this projector. A special case will then be treated in some detail. We approach this example from the perspective of path algebras and construct a dual categorified projector in the spirit of Cooper-Krushkal's recent work on the subject.