報(bào) 告 人：惠昌常 教授

報(bào)告題目：On Tachikawa’s second conjecture

報(bào)告時(shí)間：2024年03月08日（周五）下午14：00-15：00

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1508學(xué)術(shù)報(bào)告廳

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

       惠昌常，首都師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院特聘教授，博士生導(dǎo)師，教育部國(guó)家高層次人才獲得者。主要從事代數(shù)表示論的研究，在J. Rein Ang. Math., Adv. Math., Proc London Math. Soc., Math. Ann., Comm. Math. Phys，Trans Amer Math. Soc., J. Algebra, J. Pure Appl. Algebra等國(guó)際著名期刊發(fā)表論文90余篇。現(xiàn)為J. Algebra和Archiv der Mathematik的編委，曾獲教育部科技進(jìn)步二等獎(jiǎng)、德國(guó)“年輕杰出學(xué)者洪堡獎(jiǎng)”。

報(bào)告摘要：

       In the representation theory and homological algebra of finite-dimensional algebras, one of the most prominent conjectures is the long-standing and not yet solved Nakayama conjecture, saying that a finite-dimensional algebra over a field with infinite dominant dimension should be selfinjective. This conjecture is equivalent to the combination of two conjectures by Tachikawa, where the second conjecture states that an orthogonal module over a self-injective algebra should be projective. In this talk we consider Tachikawa’s second conjecture for symmetric algebras. We give a new formulation of this conjecture for symmetric algebras in terms of derived recollements of algebras. The talk presents parts of a joint work with H. X. Chen and M. Fang.