Winter School on Knot Theory and Representations

Graduate Student Workshop at UT Austin

January 11-14, 2007

Organizers: Alex Kahle and Carl Mautner

Plenary Speakers

  • Joel Kamnitzer, AIM/UC Berkeley
  • Scott Morrison, UC Berkeley

    Participants

  • Sammy Black (U of Oregon)
  • Sean Bowman
  • Orit Davidovich
  • Eric Katerman
  • Deepak Khosla
  • Parker Lowrey
  • Maksim Maydanskiy (MIT)
  • Jonathan Williams
  • Jeremy Van Horn

    The workshop took place in RLM 10.176 and began on the 11th at 9 o'clock.

    The list of topics and schedule can be found at Scott's wiki.

    More scanned notes from the workshop can be found at here.

    References and talks:

    Talk 1: Jones Polynomial and Ribbon Categories (Parker Lowrey; notes)

    Talk 2: Modular Tensor Categories and 3-manifold Invariants (Deepak Khosla; notes)

  • B. Bakalov, A. A. Kirillov; Lectures on Tensor Categories and Modular Functors, Chap. 2-3. (You can take a look at Kevin Walker's notes while you're at it.)

    • Talk 3: Chern-Simons and Witten's point of view (Alex Kahle; notes)

    Talk 4: Introduction to Khovanov Homology (Sean Bowman and Jonathan Williams with supplement by Scott; notes )

  • D. Bar-Natan; On Khovanov's categorification of the Jones polynomial.
  • M. Khovanov; An invariant of tangle cobordisms.

    • Talk 5: Bar-Natan's version and functoriality (Scott Morrison; notes)

  • D. Bar-Natan; Khovanov's homology for tangles and cobordisms.

    • Talk 6: The s-invariant (Scott Morrison; notes)

  • Rasmussen; Khovanov homology and the slice genus.

    • Talk 7: Tying Loose Ends (Joel Kamnitzer)

    Talk 8: Categorification via Category O (Carl Mautner with commentary by Joel)

  • J. Bernstein, I. Frenkel, M. Khovanov; A categorification of the Temperley-Lieb algebra and Schur quotients of U(sl(2)) via projective and Zuckerman functors.
  • C. Stroppel; Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors.
  • J. Brundan, A. Kleshchev; Represenations of shifted Yangians and finite W-algebras.

    • Talk 9: Link Invariants via Symplectic Geometry (Maksim Maydanskiy with commentary by Joel)

  • P. Seidel, I. Smith; A link invariant from the symplectic geometry of nilpotent slices.
  • I. Smith; Monodromy, vanishing cycles, knots and the adjoint quotient.
  • C. Manolescu; Nilpotent slices, Hilbert schemes, and the Jones polynomial.
  • M. Khovanov; sl(3) knot homology.

    • Talk 10: Khovanov-Rozansky Theory of Matrix Factorizations (Eric Katerman)

  • M. Khovanov, L. Rozansky; Matrix factorizations and link homology.

    • Funding was available through the generosity of Prof. Karen Uhlenbeck.

    Questions? Contact one of the organizers: Alex and Carl.