报告题目：Chains of model structures arising from modules of finite Gorenstein dimension

报告摘要：For any integer n ≥ 0 and any ring R, (PGFn, P⊥n ∩ PGF⊥) proves to be a complete hereditary cotorsion pair in R-Mod, where PGF is the class of PGF modules, introduced by J. Sˇaroch and J. ˇS´tov´ıˇcek, and PGFn is the class of R-modules of PGF dimension ≤ n. For any Artin algebra R, (GPn, P⊥n ∩ GP⊥) proves to be a complete and hereditary cotorsion pair in R-Mod, where GPn is the class of modules of Gorenstein projective dimension ≤ n. These cotorsion pairs induce two chains of hereditary Hovey triples (PGFn, P⊥n, PGF⊥) and (GPn, P⊥n , GP⊥), and the corresponding homotopy categories in the same chain are the same. It is observed that some complete cotorsion pairs in R-Mod can induce complete cotorsion pairs in some special extension closed subcategories of R-Mod. Then corresponding results in exact categories PGFn, GPn, GFn, PGF<∞, GP<∞ and GF<∞, are also obtained. As a byproduct, PGF = GP for a ring R if and only if PGF⊥ ∩ GPn = Pn for some n.

报告人简介：高楠，教授，博导，上海市“东方学者”特聘教授。研究方向为代数表示论，迄今已在《Comm.Contem.Math.》、《J.Algebra》、《Appl.Categ.Structures》、《Algebr.Represent.Theory》等国际权威期刊上发表论文30余篇。多次在一些有影响的国际国内会议上被邀请作大会报告。例如，2022年世界华人数学家大会45分钟邀请报告、第8届中日韩国际环论会议大会报告、2017年中国数学会年会分组报告、第14届全国代数学学术会议45分钟邀请报告；主持多项国家自然科学基金和2项医学领域项目。

报告时间：2024年6月8日 16：00-17：00

报告地点：同析4号楼 322会议室