报告题目1：Clifford deformations and Knorrer Periodicity Theorem
报告人：何济位教授，杭州师范大学
报告时间：2025年12月27日（周六）9:00
报告地点：20-200
报告摘要：Let $A$ and $B$ be Koszul Artin-Schelter regular algebras such that $A \otimes B$ is Noetherian. We employ the Clifford deformation to study the singularities of the Sebastiani-Thom sum denoted as $R = A \otimes B / (f \otimes 1 + 1 \otimes g)$, where both $f \in A$ and $g \in B$ are central regular elements of degree 2. It is proved that $R$ is a graded isolated singularity if and only if both $A/(f)$ and $B/(g)$ are graded isolated singularities.
The concept of a simple graded isolated singularity is introduced, along with a criterion that characterizes whether a quadratic hypersurface arising from a skew polynomial algebra is a simple graded singularity of type 0 or type 1. Then we generalize Kn\"{o}rrer's periodicity beyond commutative quadrics, expressed through triangle equivalences:
\[ \underline{\text{mcm}}R \cong \underline{\text{mcm}} A/(f) \] when $B/(g)$ is a simple graded isolated singularity of type 0, where $\underline{\text{mcm}}$ denotes the stable category of maximal Cohen-Macaulay modules; and $$\underline{\text{mcm}}R\cong \Db(\text{mmod} C_{A^!}(\theta_f)) $$ when $B/(g)$ is a simple graded isolated singularity of type 1, where $C_{A^!}(\theta_f)$ is the Clifford deformation associated with $A/(f)$.
As an application, for any noncommutative conic $A/(f)$, a triangle equivalence is established: \[\underline{\text{mcm}}\left((A/(f))^{\#}\right)\cong \underline{\text{mcm}} (A/(f)) \times \underline{\text{mcm}} (A/(f)), \] where $(A/(f))^{\#} = A[x]/(f + x^2)$ represents the double branched cover.
报告人简介：何济位，杭州师范大学数学学院教授、博士生导师，2004年毕业于浙江大学数学系，获博士学位。曾先后在复旦大学数学学院和比利时安特卫普大学从事博士后研究工作，并先后访问西班牙Almeria大学和美国华盛顿大学。浙江省高校优秀青年教师，浙江省高校中青年学科带头人，主持国家自然科学基金面上项目3项及青年基金1项，主持省部级基金4项。主要成果发表在《Trans. AMS》、《Math. Z.》、《J. Noncomm. Geometry》、《Israel J. Math.》、《J. Algebra》、《Proc. AMS》、《中国科学》等国内外主流数学期刊上。
报告题目2：Quillen equivalence for chain homotopy categories induced by balanced pairs
报告人：胡江胜教授，杭州师范大学
报告时间：2025年12月27日（周六）9:00
报告地点：20-200
报告摘要：Balanced pairs arise naturally in the realm of Relative Homological Algebra, associated with the balance of right derived functors of the Hom functor. A natural question, due to Xiao-Wu Chen, is to provide sufficient conditions under which a balanced pair of subcategories in an abelian category induces a triangle-equivalence between the corresponding chain homotopy categories of complexes. The main aim of this talk is to present new sufficient conditions addressing this question. To this end, we realize these chain homotopy categories as homotopy categories of certain model categories and give conditions that ensure a Quillen equivalence between the model categories in question. We further present applications to cotorsion triples, as well as to Gorenstein projective and Gorenstein injective modules, and to pure projective and pure injective objects. This talk is based on joint work with Wei Ren, Xiaoyan Yang, and Hanyang You.
报告人简介：胡江胜，杭州师范大学数学学院教授、博士生导师。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。2013年工作至今，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3：Homological behavior of representations over diagrams of categories
报告人：狄振兴教授，华侨大学
报告时间：2025年12月27日（周六）9:00
报告地点：20-200
报告摘要：In this talk, I will give an informal introduction to the representations over diagrams of abelian categories, which unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. I will describe important functors and adjunction relations between them, and characterize special homological objects. This talk is based on a joint work with Liping Li, Li Laing and Nina Yu.
报告人简介：狄振兴，华侨大学数学科学学院教授、博士生导师，福建省闽江学者特聘教授、入选福建省第九批创新创业人才（省引才百人计划）。主要从事模型范畴理论、相对同调理论与代数表示论等领域相关研究工作。迄今，在《Transactions of the American Mathematical Society》、《Proceedings of the Royal Society of Edinburgh. Section A. Mathematics》、《Journal of Algebra》、《Journal of Pure and Applied Algebra》等国际著名SCI刊物发表论文30余篇。2016年工作至今，主持国家自然科学基金青年基金项目1项、面上项目2项。
邀请人：魏加群