丛倾斜理论与Hall代数

本项目主要研究三角范畴的丛倾斜理论，丛代数，量子丛代数与Hall代数,它们的范畴化及其联系。具体研究三角范畴的丛倾斜对象（或子范畴）的mutation结构，丛倾斜对象的自同态代数表示理论（如（support）tau-tilting模,无限维表示等），高维Calabi-Yau-三角范畴的高阶丛倾斜理论；研究丛代数的结构与对称（如丛子代数，丛自同构群等）， 三角范畴的Hall代数， 以及用Hall代数的方法给出丛代数，量子丛代数的范畴化等等。

We will study the cluster tilting theory in triangulated categories, (quantum)cluster algebras and Hall algebras, their categorifications and relations between them. More precisely, we will study the mutation structure of cluster tilting objects (or subcategories) in triangulated categories , representations of endomorphism algebras of cluster tilting objects (such as (support) tau-tilting modules, infinite dimensional representations and so on); higher cluster tilting theory in higher Calabi-Yau triangulated categories; We will also study the structure and symmetries of cluster algebras (for examples, the cluster subalgebras and cluster automorphisms of cluster algebras), study Hall algebras of triangulated categories and give some categorifications of (quantum) cluster algebras by Hall algebra's approch.