Reading Seminar: ADE Diagrams in Mathematics

Thời gian: 14:00 đến 16:00 ngày 13/03/2026, 14:00 đến 16:00 ngày 20/03/2026, 14:00 đến 16:00 ngày 27/03/2026, 14:00 đến 16:00 ngày 03/04/2026, 14:00 đến 16:00 ngày 10/04/2026, 14:00 đến 16:00 ngày 17/04/2026, 14:00 đến 16:00 ngày 24/04/2026, 14:00 đến 16:00 ngày 08/05/2026, 14:00 đến 16:00 ngày 15/05/2026, 14:00 đến 16:00 ngày 22/05/2026,

Địa điểm: VIASM

Speakers: Tran Ngoc Hieu (VNU University of Science), Le Xuan Hoang (VNU University of Science), Nguyen Duc Khanh (VIASM)

Part 1: The appearance of ADE diagrams in the theory of Lie algebras and reflection groups.

Part 2: The McKay correspondence, the second appearance of ADE diagrams in group theory.

For the syllabus of this seminar, see here.

Abstract: ADE diagrams, in its simplest version, are just classes of graphs. But it is a structure that shows up more often than one would expect in mathematics. This seminar aims to draw some connections between ADE diagrams and seemingly different topics, including (but not limited to) Lie algebras, group theory, representation theory, and spectral graph theory. It also gives us tools to translate and navigate between various mathematical objects, such as finite groups, Lie groups, Lie algebras, graphs, matrices. Proofs will be provided when necessary; for more advanced result, the attendees should consult the references for more detail. We encourage anyone interested to join the seminar and participate in the discussion.

VI. Arnold has a dream of understanding all the mathematics related to ADE diagrams within a unifying framework. He wrote that "The next dream I want to present is an even more fantastic set of theorems and conjectures. Here I also have no theory and actually the ideas form a kind of religion rather than mathematics."