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广州数学大讲坛第25期

赵明慧、常文、阮诗佺等副教授学术报告

时间:2021-06-15 点击数:

北京林业大学赵明慧副教授学术报告


报告题目:Constructions of highest weight modules of double Ringel-Hall algebras via functions

时间:2021年6月17日(星期四)09:45-12:00

地点:腾讯会议ID 836720889

报告人:北京林业大学赵明慧副教授

报告摘要:Zheng Hao studied the bounded derived categories of constructible sheaves on some algebraic stacks consisting of the representations of a framed quiver and categorified the integrable highest weight modules of the corresponding quantum group by using these categories. In this talk, we shall introduce a generalization of Zheng's work and give realizations of highest weight modules of a certain subalgebra of the double Ringel-Hall algebra of a finite quiver via spaces of functions on representation varieties of the framed quiver.

报告人简介:赵明慧,北京林业大学副教授,2013年博士毕业于清华大学。研究领域是代数表示论,主要从事Hall代数,量子群等相关问题的研究。目前在J. Algebra,Algebr. Represent. Theory等国际重要学术期刊上发表论文数篇。



陕西师范大学常文副教授学术报告


报告题目:Reductions for the derived category of a gentle algebra

时间:2021年6月18日(星期五)09:45-12:00

地点:腾讯会议ID 887756410

报告人:陕西师范大学常文副教授

报告摘要:A graded gentle algebra gives rise to a graded dissection of an oriented graded marked surface with boundary into polygons and the finite dimensional derived category of the graded gentle algebra has a geometric interpretation in terms of this surface, where the graded gentle algebra is viewed as a differential graded algebra with zero differential. This provides us some new tools to study the derived category of graded gentle algebras, by using the combinatorics of the surface. In this talk, I will show that the cutting of the graded marked surface gives us a geometric realization of the reductions of the graded gentle algebras and the corresponding derived categories. In fact, the cutting gives us a recollement of derived categories of three graded gentle algebras. So in some sense, we also obtain a ‘recollement of graded surfaces’. This is ongoing joint work with Sibylle Schroll and Haibo Jin.

报告人简介:常文,陕西师范大学副教授,2015年博士毕业于清华大,曾受国家留学基金委资助于2018年访问美国康涅狄格大学一年。研究兴趣包括代数表示论、同调代数、丛代数等。主持完成国家自然科学基金青年项目一项,现主持陕西省青年人才计划项目一项。目前在 J. Algebra,Math. Z.,Pacific J. Math., Adv. in App. Math. 等国际重要期刊上发表论文多篇。



厦门大学阮诗佺副教授学术报告


报告题目:t-stabilities for a weighted projective line

时间:2021年6月19日(星期六)09:45-12:00

地点:腾讯会议ID 678560289

报告人:厦门大学阮诗佺副教授

报告摘要:In this talk we will focus on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the finest t-stabilities on certain triangulated category and, describe the semistable subcategories and last HN-triangles for coherent sheaves in $D^b(\coh\X)$, which is the bounded derived category of coherent sheaves on the weighted projective line $\X$ of weight type (2). Furthermore, we show the existence of a t-exceptional triple for $D^b(\coh\X)$. As an application, we obtain a result of Dimitrov-Katzarkov which states that each stability condition $\sigma$ in the sense of Bridgeland admits a $\sigma$-exceptional triple for the acyclic triangular quiver $Q$. This result plays an important role in the proof of Dimitrov-Katzarkov that the space of stability conditions associated to $Q$ is connected and contractible. This is joint work with Xintian Wang.

报告人简介:阮诗佺,厦门大学bg真人副教授。现主持国家自然科学基金青年基金、中央高校基金各一项,曾获得德国洪堡基金、中国博士后面上基金。2014-2017年清华大学丘成桐数学科学中心博士后,2017-2018比勒菲尔德大学博士后。在Mathematische Zeitschrift、Annales de l'Institut Fourier、International Mathematics Research Notices、Journal of Algebra、Journal of Pure and Applied Algebra等国际重要学术期刊发表论文10余篇。



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