|Affiliation||The University of Tokyo|
|Time||Jan 9 13:00~13:40|
|Title||Quantum and homological representations of braid groups|
We describe a relation between homological representations of braid groups studied by Lawrence, Krammer and Bigelow and quantum representations appearing as the monodromy of KZ equations for generic parameters. In the case of special parameters these representations are extended to quantum representations of mapping class groups. We describe the images of such representations and show that the images of any Johnson subgroups contain non-abelian free groups if the genus and the level are sufficiently large. The last part is a joint work with Louis Funar.