Distinguished Lecture Series in Representation Theory and Mathematical Physics
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Ivan Dimitrov - Root systems, generalizations and applications, Room 403.
2026, May 19 and 21 (3-4pm),
2026, June 1, 3 and 5 (4-5pm).
Abstract. Root systems were introduced by Wilhelm Killing in 1889 as a tool for classifying Lie algebras. Since then, they have become ubiquitous, appearing in various contexts in seemingly unrelated areas of Mathematics. In this lecture series, I will introduce and study root systems and will define a generalization of root systems. I will explain how this more general structure applies to various problems, e.g. hyperplane arrangements. Finally, I will introduce and study inversion sets of roots.
The exposition will be mostly self-contained, assuming Linear algebra and some Group theory background.
Key words. Root systems, Coxeter groups, Hyperplane arrangements, Inversion sets of roots
Gordana Todorov - Algebras and categories: Auslander, Cluster, Preprojective and Higher Version of Those, Room 403.
2026, May 18-22 (4-5pm), Room 403.
Topics:
Quiver representations, Gabriel, Dlab, Ringel — Dynkin diagrams, Auslander-Reiten theory.
Cluster algebras and cluster categories.
Higher Auslander algebras and cluster tilting subcategories.
Preprojective algebras and higher preprojective algebras.
Preprojective structure on subcategories.
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