江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：Blocks with a single automorphism orbit of irreducible Brauer characters
报告地点：数学学院B303
报告摘要：Fix a prime $p$，Let $G\trianglelefteq\tilde G$ be finite groups such that $|\tilde G:G|$ is a power of $p$, and let $\tilde b$ be a block of $\tilde G$ with abelian defect groups covering a block $b$ of $G$. We prove that $\tilde b$ is inertial whenever $\IBr(b)$ is a single $\Aut(G)_b$-orbit. This verifies the {abelian-defect case of the Kessar--Linckelmann conjecture}. As a key ingredient, we further show that a block of a finite quasisimple group with a single automorphism orbit of irreducible Brauer characters has abelian defect groups. As applications, we prove the blockwise Alperin weight conjecture for blocks with exactly one irreducible Brauer character and establish Puig's nilpotency conjecture.
个人简介：周远扬，华中师范大学教授，杰青。国内有限群表示论顶尖专家，湖北省政协第十三届常务委员，湖北省数学会副理事长，德国洪堡学者，教育部新世纪优秀人才，2016年国家杰出青年基金获得者。