I'm working on quantized enveloping algebras. These algebras have been investigated in depth by George Lusztig and Masaki Kashiwara. Moreover, my recent research results have applications on Lusztig's construction for the canonical basis. Since Prof. Lusztig will be present, I'm sure that I'll benefit a lot by joining the forum. I hope to talk with Prof. Lusztig as well as other people working in similar areas and share our ideas. I firmly believe that such communications will facilitate our research on quantized enveloping algebras and many other mathematical topics.

Beijing Institute of Mathematical Sciences and Applications

My research concerns quantum algebras. I work specifically with the quantized enveloping algebra for affine sln. In recent years, I have been studying this algebra using an embedding into a q-shuffle algebra due to Marc Rosso. For the case n=2, here we denote the positive part of this algebra by Uq+. I have obtained several results on Uq+ using the Rosso embedding. One of these results is a uniform approach to three PBW basis for Uq+, due to Ilaria Damiani, Jonathan Beck, and Paul Terwilliger respectively. Currently, I'm exploring the applications of these results on three topics: Lusztig's construction for the canonical basis, boundary Yang-Baxter equations, and distance-regular graphs.