Monday, February 17, 2020
Time  Items 

All day 

4:00pm 
02/17/2020  4:00pm The ideal boundary of a negatively curved manifold naturally carries two types of measures. On the one hand, we have conditionals for equilibrium (Gibbs) states associated to Hoelder potentials; these include the PattersonSullivan measure and the Liouville measure. On the other hand, we have stationary measures coming from random walks on the fundamental group. Location:
DL431
02/17/2020  4:30pm Drinfeld proved that the Yangian Yg of a complex semisimple Lie algebra g gives rise to solutions of the quantum YangBaxter equations on irreducible, finitedimensional representations of Yg, which are rational in the spectral parameter. This result was recently extended by MaulikOkounkov for KacMoody algebras corresponding to quivers, and representations arising from geometry.
Surprisingly perhaps, this rationality ceases to hold if one considers arbitrary finitedimensional representations of Yg, at least if one requires such solutions to be natural with respect to the representation and compatible with tensor products.
I will explain how one can instead produce meromorphic solutions of the QYBE on all finitedimensional representations by resumming Drinfeld’s universal Rmatrix R(s) of Yg. The construction hinges on resumming the abelian part of R(s), and on realizing its lower triangular part as a twist conjugating the standard coproduct of Yg to its deformed Drinfeld coproduct.
This is joint work with Sachin Gautam and Curtis Wendlandt, and is based on arXiv:1907.03525 Location:
LOM 214
