Singular equivalences and the Auslander-Reiten conjecture-陈一萍教授（武汉大学）
报告题目：Singular equivalences and the Auslander-Reiten conjecture
摘要：Let k be a field, and A be a finite dimensional k-algebra. The Auslander-Reiten conjecture (or generalized Nakayama conjecture) says that every finitely generated left A-module M with A+M being orthogonal should be projective. The conjecture is still open now, and plays a central role in the representation theory of algebras. And it is closely connected with the celebrated Nakayama conjecture and the finitistic dimension conjecture.
In this talk, we will discuss this behaviors of this conjecture under certain singular equivalences induced by adjoint pairs. As an application, we prove that this conjecture holds for all skew-gentle algebras (J. Algebra 623 (2023), 42-63 and arXiv: 2212.06467).