讲座人简介：段冰，兰州大学澳门新葡平台app官网副教授。主要从事丛代数和量子仿射代数、表示论等相关方面的研究，目前在IMRN、J. Lond. Math. Soc.、Math. Z.、J. Algebra等国际重要期刊上发表论文数篇。

讲座简介：In this talk, I will report some new results on the classification of real simple modules over a simply-laced quantum affine algebra and categorifications of cluster algebras. Let C be the category of finite-dimensional modules over a simply-laced quantum affine algebra Uq(g). For certain small subcategories of C whose Grothendieck rings admit cluster algebra structures of finite type, we completely classify all real simple modules in terms of their highest ell-weight monomials. The real simple modules of type D and type E are new, and our treatment for type A is different with the one of Brito-Chari. We are using our method to study more real simple modules. This is ongoing joint work with Professor Ralf Schiffler.