Winter School on Knot Theory and Representations
Graduate Student Workshop at UT Austin
January 11-14, 2007
Kahle and Carl Mautner
Scott Morrison, UC
Sammy Black (U of Oregon)
Maksim Maydanskiy (MIT)
Jeremy Van Horn
The workshop took place in RLM 10.176 and began on the 11th at 9
The list of topics and schedule can be found at Scott's wiki.
More scanned notes from the workshop can be found
References and talks:
Talk 1: Jones Polynomial and Ribbon Categories (Parker Lowrey; notes)
Talk 2: Modular Tensor Categories and 3-manifold Invariants (Deepak
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;
D. Bar-Natan; On Khovanov's
categorification of the Jones polynomial.
M. Khovanov; An invariant of
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
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.
Manolescu; Nilpotent slices,
Hilbert schemes, and the Jones polynomial.
M. Khovanov; sl(3) knot
Talk 10: Khovanov-Rozansky Theory of Matrix Factorizations (Eric
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.