Schedule

## May 10 -- 25, 2007 Kyoto University

Program

First Week (at Fac.of Science Bldg.No.3)

 5/10 (Thu.) 13:30 -- 14:30 Aaron Lauda (Columbia) Jones polynomial and its extension to tangles 15:00 -- 16:30 Dror Bar-Natan (Toronto) Overview of Khovanov Homology 5/11 (Fri.) 10:00 -- 12:00 Aaron Lauda A homological invariant of tangles and tangle cobordisms (with break) 14:00 -- 15:00 Dror Bar-Natan Overview of Khovanov Homology, II 15:30 -- 16:30 Aaron Lauda $sl(3)$ link homology ( math.QA/0304375 )
Second Week (at RIMS)

 5/14 (Mon.) 9:30 -- 10:30 Scott Morrison (Berkeley) An introduction to Khovanov homology 11:00 -- 12:00 Lev Rozansky (North Carolina) An introduction to matrix factorizations 13:30 -- 14:30 Ciprian Manolescu (Columbia) Knot Floer homology I 15:00 -- 16:00 Sergei Gukov (Caltech) Link Homologies and Open Gromov-Witten Invariants 5/15 (Tue.) 9:30 -- 10:30 Scott Morrison More about Khovanov homology: genus bounds and spectral sequences the easy way 11:00 -- 12:00 Lev Rozansky Categorification of the $SU(N)$ HOMFLY-PT polynomial 13:30 -- 14:30 Ciprian Manolescu Knot Floer homology II 15:00 -- 16:00 Sergei Gukov Gauge Theory and Categorification 16:30 -- 17:30 Marko Stosic (Inst. Super. T\'ec.) Homology of torus knots and links 5/16 (Wed.) 9:30 -- 10:30 Joel Kamnitzer (Berkeley) Knot homology via derived categories of coherent sheaves: motivation and geometric setup 11:00 -- 12:00 Raphael Rouquier (Oxford) $sl(2)$-categorification 13:30 -- 14:30 Catharina Stroppel (Glasgow) An introduction into representation theory of Lie algebras 15:00 -- 16:00 Marco MacKaay (Algarve) Towards an $sl(n)$ link homology theory using foams (joint work with Marko Stosic and Pedro Vaz) 16:30 -- 17:30 Alexander Shumakovitch (Washington) Naive Categorification of the Skein $sl(N)$ Polynomial
 5/17 (Thu.) 9:30 -- 10:30 Sabin Cautis (Harvard) Knot homology via derived categories of coherent sheaves: spherical twists and relation to Khovanov homology 11:00 -- 12:00 Raphael Rouquier Higher representation theory 13:30 -- 14:30 Catharina Stroppel Khovanov's algebra $H_n$ appearing naturally in representation theory 15:00 -- 16:00 Joshua Sussan (Yale) Category ${\mathcal O}$ and the colored Jones polynomial 5/18 (Fri.) 9:30 -- 10:30 Dror Bar-Natan The Virtues of Being an Isomorphism , Abstract 11:00 -- 12:00 Lev Rozansky Categorification of the $SO(2N)$ Kauffman polynomial 13:30 -- 14:30 Peter Ozsvath (Columbia) Knot Floer homology III 14:45 -- 15:45 Ciprian Manolescu Knot Floer homology IV
(We must evacuate the room at 16:00.)

Third Week (at Fac.of Science Bldg.No.3)
 5/21 (Mon.) 10:30 -- 11:30 Susumu Ariki (RIMS) Integrable ${\dot U}(\hat{sl}_e)$-modules via cyclotomic Hecke algebras 13:30 -- 14:30 Peter Ozsvath Knot Floer homology V 15:00 -- 16:00 Kokoro Tanaka (Gakushuin) Khovanov-Jacobsson numbers of surface-knots and their extension 5/22 (Tue.) 9:30 -- 10:30 Catharina Stroppel Invariants of tangles and Cobordisms: From Jones to Kauffman and BMW 11:00 -- 12:00 Yasuyoshi Yonezawa (Nagoya) Matrix factorizations and planar diagrams in MOY link invariant (Big lunch break !) 15:00 -- 16:00 Peter Ozsvath Knot Floer homology VI 16:30 -- 17:00 Radmila Sazdanovic (George Washington) Torsion in Chromatic Graph Cohomology 5/23 (Wed.) 9:30 -- 10:30 Joel Kamnitzer The affine Grassmannian and the geometric Satake correspondence I 11:00 -- 12:00 Scott Morrison Functoriality and duality in Khovanov homology (free afternoon) Mikhail Kapranov (Yale) give a colloquium talk at 14:40 at RIMS 402 5/24 (Thu.) 9:30 -- 10:30 Joel Kamnitzer The affine Grassmannian and the geometric Satake correspondence II 11:00 -- 12:00 Stephan Wehrli (Columbia) Mutation invariance of Khovanov homology over ${\mathbf Z}/2{\mathbf Z}$

Abstract of Dror Bar-Natan's talk:

I'm over forty, I'm a full professor, and it's time that I come out of the closet. I don't understand quantum groups and I never did. I wish I could tell you in my talk about one of the major stumbling blocks I have encountered - I don't understand the amazing Etingof-Kazhdan work on quantization of Lie bialgebras. But hey, I can't tell you about what I don't understand! So instead, I will tell you about how I hope to understand the Etingof-Kazhdan work, one day, as an isomorphism between a topologically defined space and a combinatorially defined one. The former would be the unipotent completion of a certain algebra of virtually-knotted (trivalent?) graphs. The latter would be the associated graded space of the former.

I'll start and spend a good chunk of my time with an old but not well known analogy, telling you why a Drinfel'd associator, the embodiment of the spirits of all quasi-Hopf algebras, is best viewed as an isomorphism between the unipotent completion of the algebra of honestly-knotted trivalent graphs and its associated graded space, a certain combinatorially-defined algebra of chord diagrams. A few words will follow, about the relationship between diagrammatic Lie bialgebras and finite type invariants of virtual knots.

Contact H.~Nakajima (nakajima@math.kyoto-u.ac.jp) for any question.