BIMSA > Algebra Seminar Algebra Seminar On the categorification of the cluster variety of triples of flags
On the categorification of the cluster variety of triples of flags
Organizer
Yu Qiu
Speaker
Miantao Liu
Time
Thursday, March 26, 2026 8:00 AM - 9:00 AM
Venue
Online
Online
Zoom 442 374 5045 (BIMSA)
Abstract
The cluster variety of triples of flags (associated with a split simple Lie group of Dynkin type Delta) plays a key role in higher Teichmuller theory as developed by Fock-Goncharov, Jiarui Fei, Ian Le, ... and Goncharov--Shen. We refer to it as the basic triangle associated with Delta. For simply laced Delta, we construct and study a Higgs category, in the sense of Yilin Wu, which we expect to categorify the basic triangle. This category  is a certain exact differential graded (=dg) category, in the sense of Xiaofa Chen, which is Frobenius and stably 2-Calabi-Yau.  We show that it has indeed the expected cyclic group symmetry and that its derived category has the expected braid group symmetry. A key ingredient in our construction is a conjecture by Merlin Christ.