2020年代数表示论青年学者系列报告（线上）
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：陈一萍、卢明、任伟、何济位、陈银
：2020-07-10 15:30
：腾讯会议App
系列报告1
Speaker：Dr. Yiping Chen
Wuhan University
Title: Recollements, Hochschild cohomology and support varieties
Time：10 July 2020,15:30
Location： 腾讯会议App（会议号：479 931 865）
Abstract: Hochschild cohomology of finite dimensional algebras is a fundamental homological invariant, used for instance to define and compute support varieties of modules or complexes. This needs a non-trivial assumption known as the (Fg) condition. In this talk, we develop a general theory providing tools to compare Hochschild cohomology of two given algebras, validity of the (Fg) condition and support varieties theoretically in terms of connections between derived module categories.This is a joint work with Steffen Koenig.
Speaker Introduction：陈一萍，武汉大学数学与统计学院副教授，研究方向为代数表示论，主持过国家自然科学基金青年基金、教育部博士点新教师基金。主要从事三角范畴与导出等价、Hochschild上同调与Support variety理论的研究，目前已经在Math. Z., Proc. Roy. Soc. Edinburgh Sect. A, J. Algebra, J. Pure Appl. Algebra, Algebr. Represent. Theory等数学杂志上发表多篇高水平的学术论文。
陈一萍副教授2011年博士毕业于北京师范大学数学科学学院，2013年受邀在第十三届全国代数学会议上做40分钟报告，2015年至2018年期间，先后多次受德国DFG项目和国家留学基金委资助访问德国斯图加特大学。
系列报告2
Speaker：Dr. Ming Lu
Sichuan University
Title: Hall algebra realization of i-quantum groups
Time：17 July 2020,15:30
Location： 腾讯会议App（会议号：813 200 235）
Abstract: A quantum symmetric pair consists of a quantum group and its coideal subalgebra (called an i-quantum group). A quantum group can be viewed as an example of i-quantum groups associated to symmetric pairs of diagonal type. In this talk, we present a new Hall algebra construction of i-quantum groups. A new class of 1-Gorenstein algebras (called i-quiver algebras) arising from quivers with involutions is introduced, and their singularity categories are characterized by the existence of tilting objects. Their Ringel-Hall algebras are isomorphic to i-quantum groups. This is joint work with Weiqiang Wang (University of Virginia).
Speaker Introduction：卢明，四川大学数学学院助理教授。2013年7月毕业于四川大学数学系，获理学博士学位。主要从事同调代数、导出范畴、i-量子群的研究，目前已经在Transformation Groups, Journal of Algebra，Algebra and Representation Theory，Nagoya J. Math等数学杂志上发表多篇高水平的学术论文。
系列报告3
Speaker：Dr. Wei Ren
Chongqing Normal University
Title: Cotorsion pairs and stable categories over triangular matrix rings
Time：24 July 2020,15:30
Location： 腾讯会议App（会议号：807 303 588）
Abstract: Cotorsion pairs are analogs of the classical torsion pairs where Hom is replaced by Ext. The complete cotorsion pairs have been widely understood as suitable contexts on approximation theory; relationships between cotorsion pairs and t-structures and co-t-structures of triangulated categorie have been presented; correspondence between cotorsion pairs and Quillen model structures has been discovered.
In this talk, we focus on cotorsion pairs of modules over a triangular matrix ring T. When T is left-Gorenstein with U a compatible A-B-bimodule, we find subcategories of Gorenstein projective T-modules and construct some complete cotorsion pairs. As applications, it is shown that there are equivalences between stable categories of Gorenstein projective modules over A and B, and corresponding homotopy categories of model structures on T-Mod induced by these cotorsion pairs. Finally, a recollement of Zhang can be generalized slightly where the modules are not necessarily finitely generated.
Speaker Introduction：任伟，重庆师范大学数学科学学院副教授，研究方向为同调代数，主持国家自然科学青年基金项目及面上项目、博士后基金项目及重庆市自然科学基金项目等。主要从事Gorenstein 同调代数、三角范畴、模型结构的研究，在J. Algebra, Sci. Math. China, Appl. Categorical Struct. 等杂志上发表多篇学术论文。 任伟副教授2013年博士毕业于西北师范大学数学科学学院，2013年受邀在第十三届全国代数学会议上做40分钟报告。
系列报告4
Speaker：Prof. Jiwei He
Hangzhou Normal University
Title: Cohen-Macaulay modules of noncommutative quadric hypersurfaces
Time：31 July 2020,15:00
Location： 腾讯会议App（会议号：943 245 941）
Abstract: Let $S$ be a Koszul Artin-Schelter regular algebra, and let $z\in S$ be a central regular element of degree 2. The quotient algebra $A=S/Sz$ is usually called a noncommutative quadric hypersurface. In this talk, we will provide a method to verify whether a noncommutative quadric hypersurface is an isolated singularity, and a method to compute indecomposable maximal Cohen-Macaulay modules. We also introduce the notion of right pre-resolutions (quasi-resolutions) for noncommutative isolated singularities, which is a weaker version of quasi-resolutions introduced by Qin-Wang-Zhang. We show that right quasi-resolutions for noetherian bounded below and locally finite graded algebra with right injective dimension 2 are always Morita equivalent. For a noncommutative quadric hypersurface which is also a noncommutative isolated singularity, we show that it always admits a right pre-resolution. The talk is based on a joint work with Yu Ye.
Speaker Introduction：何济位，杭州师范大学教授，2004年毕业于浙江大学数学系，获博士学位。2004年至2012年先后在复旦大学和比利时安特卫普大学从事博士后研究工作，并先后访问过西班牙Almeria大学和美国华盛顿大学。浙江省“151人才”第三层次培养对象，省高校优秀青年教师，省高校中青年学科带头人培养对象。主持国家自然科学基金面上项目2项，青年基金1项，省部级基金4项。主要研究领域为非交换代数，在Trans. AMS、Math. Z.、J. Noncomm. Geometry、J. Algebra等数学期刊发表学术论文30余篇。
系列报告5
Speaker：Prof. Yin Chen
Nantong University
Title: Modular invariants of finite glueing groups
Time：31 July 2020,16:05
Location： 腾讯会议App（会议号：943 245 941）
Abstract: Motivated by the works of Kuhn-Mitchell (1986), Hewett (1996), and Huang (2012), we introduce a notion of glueing groups and develop a systematic study on modular invariants of finite glueing groups. As the main application, we are able to calculate the modular invariant rings of the maximal parabolic subgroups and Sylow subgroups of finite symplectic groups. This a joint work with R. James Shank and David L. Wehlau.
Speaker Introduction：陈银，男，理学博士，南通大学理学院校聘教授；现为中国数学会及美国数学会会员、MR数学评论及zbMATH评论员。主要研究领域为：有限群的不变量理论、交换代数及李理论；其研究成果已经在Manuscripta Math.、 J. Algebra、J. Pure Appl. Algebra等杂志上发表。
陈银教授曾主持国家自然科学基金委青年基金项目及天元基金项目的研究；也曾获得加拿大数学会、中国数学会的年会的分组邀请报告；其国际学术访问获得加拿大NSERC、国家外专局、国家留学基金委等机构的资助。
联系人：林亚南教授，陈健敏教授，阮诗佺助理教授
