29.01.2026, Vorträge Fachbereich Mathematik: 10:00-10:50 Uhr: Buyan Li, Tsinghua University, 11:00-11:50 Uhr: Yixin Lan, MPI Bonn

10:00-10:50 Uhr: Buyan Li, Tsinghua University, zum Thema: "Root Category and Simple Groups of Lie Type" Abstract: Ringel used the representation theory of finite-type hereditary algebra and Hall polynomials to obtain the positive part of the simple Lie algebra. Peng and Xiao generalized Ringel's result to root category and obtained the whole Lie algebra. Based on their constructions, we construct the compact real form of the complex semisimple Lie algebra, and the Chevalley group of the root category, as well as its maximal compact subgroup. On the other hand, Lusztig used the modified quantum group and its canonical basis to obtain the reductive group and its coordinate ring O. By combining these, we explore how the classical theory of compact Lie groups, such as Peter-Weyl theorem and Plancherel theorem, can be recovered completely. This talk is based on a joint work with Prof. Jie Xiao. 11:00-11:50 Uhr: Yixin Lan, MPI Bonn, zum Thema: "From Lusztig's canonical bases to Nakajima quiver varieties“