Hopf algebras, their representations, applications, and categorifications

Semester: | Fall 2008 | |

Call number: | 53048 | |

Room/Time: | MW 2:40pm--3:55pm, 307 Math | |

Instructor: | Mikhail Khovanov | |

Office: | 517 Math | |

Office Hours: | Walk-in or by appointment | |

E-mail: | khovanov@math.columbia.edu | |

Discussions: | TBA | |

TA: | Daniel Krasner, dkrasner@math.columbia.edu | |

Webpage: | www.math.columbia.edu/~khovanov/topics2008 | |

G.Kuperberg, Non-involutory Hopf algebras and 3-manifold invariants

P.Cartier, A primer of Hopf algebras

B.Pareigis, Hopf algebras, algebraic, formal, and quantum groups. This is chapter 2 of his book Lectures on quantum groups and noncommutative geometry

J.Bernstein, Sackler lectures on quantum groups and TQFTs.

A.Ram, A survey of quantum groups (gunzipped ps file)

V.F.R.Jones, In and around the origin of quantum groups

O.Schiffmann, Lectures on Hall algebras

J.Chuang and R.Rouquier Derived equivalences for symmetric groups and sl(2)-categorification

A.Lauda,A categorification of quantum sl(2)

A.Lauda and M.Khovanov,A diagrammatic approach to categorification of quantum groups I

C.Kassel, Homology and cohomology of associative algebras - A concise introduction to cyclic homology

D.Milicic, Lectures on derived categories

P.Etingof and students, Lectures and problems in representation theory covers representations of algebras, finite groups, and quivers.

H.Barcelo and A.Ram, Combinatorial representation theory

D.Gaitsgory, Geometric Representation theory Notes for a course on highest weight categories.

C.Blanchet, Introduction to quantum invariants of knots and links

K.Walker, On Witten's 3-manifold invariants

G.Kuperberg, Spiders for rank 2 Lie algebras

M.Freedman, C.Nayak, K.Walker, Z.Wang, On Picture (2+1)-TQFTs

C.Blanchet, Introduction to quantum invariants of 3-manifolds, topological quantum field theories, and modular categories