Geometric interactions between bricks and other families of indecomposable modules I

系列报告

题目：Geometric interactions between bricks and other families of indecomposable modules I

时间地点：7月26日 下午15:00-16:00， 36号楼510.

题目：Geometric interactions between bricks and other families of indecomposable modules II

时间地点：7月29日 下午15:00-16:00， 36号楼510.

报告人: Kaveh Mousavand (Okinawa Institute of Science and Technology, Japan)

摘要: In these talks, we will primarily focus on some applications of geometric tools in representation theory of finite dimensional algebras. In particular, we use some standard geometric facts to provide further insights into the study of some classical and modern conjectures. More precisely, after a quick recollection of some rudiments, including the classical Brauer-Thrall conjectures (now theorems) and some well-known geometric tools, I present some modern brick counterparts of the Brauer-Thrall conjectures. Then, I explain how our geometric treatments, together with some reduction techniques, allow us to settle these open conjectures for some families of algebras. We further use this approach to translate our open conjectures on bricks into the study of some other important family of objects in representation theory, and to describe the connections between our brick-Brauer-Thrall conjectures and some analogous conjectures that have recently appeared in the literature. This is partially based on my recent joint work with Charles Paquette.

报告人简介: Mousavand教授2020年在加拿大蒙特利尔大学获得博士学位，师从Hugh Thomas 教授。2020-2023年在加拿大Queen's University数学统计学院从事博士后工作， 目前在日本冲绳科技研究院(OIST)表示论与代数组合研究室工作。他的研究领域涉及代数表示论、模空间理论、丛代数以及代数组合。Mousavand教授与许多国际知名数学家有广泛的合作，曾在Journal of the London Mathematical Society, Journal of algebra以及Canadian Journal of Mathematics等国际著名SCI期刊发表高水平论文。