导出范畴与Gorenstein同调理论天元数学讲习班

The research about derived categories and Gorenstein homological theory is a research hotspot in homological algebra, the representation theory of algebras, algebraic geometry and other fields. However, there is still a gap between the domestic research level and the international advanced level. In order to improve the academic level of domestic scholars and strengthen the cooperation and exchange between domestic scholars and international experts, we try to apply this project.. In this project, authoritative experts will be invited to teach basic and professional courses, and international authoritative experts will be invited to conduct academic reports in the field of professional frontier topics, so as to discuss with domestic outstanding scholars of algebras. The workshop will adopt the way of teaching, academic report, discussion and cooperation in writing papers, so as to effectively study and exchange. Through this workshop, domestic young scholars can consolidate the basic knowledge of derived categories and Gorenstein homological theory, understand the research frontier of related issues, and select the interest points as future research topics.. It is expected that with the support of the Tianyuan Foundation of Mathematics, through the implementation of this project, it can promote the domestic research on derived categories, Gorenstein homological theory and their applications, and enhance the status of domestic scholars in related fields.

导出范畴与Gorenstein同调理论的研究是当前同调代数、代数表示论、代数几何等领域的研究热点之一。但是国内相关领域的研究水平与国际先进水平相比尚有差距。为了提高国内学者的学术水平，加强国内学者与国际相关专家的合作交流，我们申请本项目。. 本项目拟邀请权威专家讲授基础课和专业课，并邀请国际权威专家来华就国际前沿课题做学术报告，与国内优秀代数学者共同探讨。讲习班拟采取授课、学术报告、研讨以及合作撰写论文的方式，有效地进行学习和交流。通过本次讲习班，国内青年学者可夯实导出范畴与Gorenstein同调理论的基础知识，了解相关问题的研究前沿，并选出感兴趣的部分作为以后的研究课题。. 期待着在数学天元基金的资助下，通过本项目的实施，能够带动国内导出范畴与Gorenstein同调理论及其应用方面的研究，提升国内学者在相关领域的地位。

为推动和繁荣我国在导出范畴与Gorenstein同调理论领域的研究，提高和促进我国导出范畴与Gorenstein同调理论的整体研究水平，我们于2022年7月17日-2022年8月5日以线上的方式为国内的研究生和青年学者举办了“2022导出范畴与Gorenstein同调理专题讲习班暨学术研讨会”。我们邀请了6位知名专家讲授了5门共80学时的关于导出范畴与Gorenstein同调理论的课程，邀请了20名相关领域的国内外知名专家为讲习班做专题报告，并组织开展了研究生论坛，有10名博士生做学术报告。