报告题目1：Wakamatsu tilting modules and homological invariants
报告人：胡江胜教授，杭州师范大学
报告时间：2025年4月26日（周六）9:00
报告地点：20-308
报告摘要：Wakamatsu tilting modules are one of many important generalizations of tilting modules and may have infinite projective dimension. They are of particular interest in algebraic representation theory and homological algebra due to their central role in Wakamatsu tilting conjecture proposed by Beligiannis and Reiten. In this talk, we present some homological properties of Wakamatsu tilting modules with applications to the Wakamatsu tilting conjecture and homological invariants.
报告人简介： 胡江胜，杭州师范大学教授。主要从事同调代数与代数表示理论等领域的研究，研究领域涉及逼近理论、高维同调理论、Gorenstein同调理论与复形的相对上同调理论等。主持国家自然科学基金面上项目、青年项目、数学天元基金项目等科研项目多项。在Israel J. Math., Canad. J. Math., Quart. J. Math., J. Algebra, J. Pure Appl. Algebra, Sci. China Math.等国内外著名数学期刊上发表学术论文40余篇。
报告题目2：(Generalized) Generating Hypothesis in t-Categories
报告人：扶先辉教授，东北师范大学
报告时间：2025年4月26日（周六）9:00
报告地点：20-308
报告摘要：Suppose (D;(D≤0,D≥0)) is a t-category whose heart is denoted as A. A morphism f:X→Y in D is said to be a ghost morphism provided that Hn(f)=0,∀n∈Z, where H0(−) is the cohomology functor induced by the t-structure (D≤0,D≥0). In this talk, I will prove a version of the n-fold Generalized Generating Hypothesis: If (D≤0,D≥0) is non-degenerate and countably cocomplete such that A has enough projective objects and every Yoneda extension group YExtAq(M,N) is canonically isomorphic to HomD(M,N[q]), then proj.dimA+1 is precisely the supremum of how many concatenating ghost morphisms can compose non-trivially. I will give a very detailed analysis of the cases where n=1 and 2, with very interesting relations with semisimple and hereditary triangulated categories. As an application, we will study the famous n-fold Generating Hypothesis under the circumstances where our t-category is generated by a rigid compact generator G. We will demonstrate that, under some reasonable assumptions, the t-structure induced by G in the ambient triangulated category can be restricted to the full subcategory of all compact objects; in particular, if G is a tilting object such that End(G) is a right coherent ring of finite weak global dimension, then w.gl.dimEnd(G)+1 is equal to the supremum of how many concatenating ghost morphisms between compact objects can compose non-trivially. This talk is based on a joint work with Dr. Yifan Chen.
报告人简介： 扶先辉，东北师范大学数学与统计学院教授、博士生导师。研究领域为同调代数和K-理论，现致力于逼近理论及其相关课题的研究，研究工作发表于Adv. Math., Proc. London Math. Soc., J. Algebra, J. Pure Appl. Algebra等期刊。多次主持国家自然科学基金项目，并曾在第十三届全国代数学学术会议和第八届中日韩国际环论会议做大会报告。
报告题目3：Non-commutative cluster algebras from orbifolds and quantum cluster algebras
报告人：黄敏副教授，中山大学
报告时间：2025年4月26日（周六）9:00
报告地点：20-308
报告摘要：In this talk I will introduce a class of non - commutative algebras from orbifolds with cluster structures. In the unpunctured case, I will also show that there is a surjective algebra homomorphism from the non-commutative algebra to the quantum cluster algebra. This talk is based on joint work with Berenstein and Retakh.
报告人简介：黄敏，中山大学逸仙学者计划新锐学者、博士生导师。2017年获浙江大学理学博士学位，2017-2020年于加拿大Sherbrooke大学和香港大学从事博士后研究。2020年入职中山大学任“百人计划”副教授，从事代数学方向研究，在丛代数理论、代数表示理论和拓扑联系方面成果颇丰。与李方教授合著《丛代数理论导引》，在Adv. Math., Trans. AMS., Selecta. Math.等国内外重要学术期刊发表论文10余篇，主持国家自然科学基金2项。