中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人：古 星 博士（Max Planck Institute for Mathematics）
题 目：Topological Brauer Groups, Postnikov Systems, And Twisted K-Theory
时 间：2021.05.09（星期日），09:30-11:30
地 点：数学院南楼N224室 腾讯会议：815 999 228
摘 要：This talk is an attempt to give a comprehensive account on the topological period-index problem (TPIP).I will explain the relation between TPIP and the period-index problem in algebraic geometry, especially over the base field C, through the works of Antieau-Williams and Crowley-Grant on TPIP over 6-dimensional finite CW-complexes and 6-dimensional spinC closed manifolds.The main tool for studying TPIP over finite CW-complexes are the Post-nikov systems of the classifying spaces of certain compact Lie groups, which is another major topic of this talk. Finally I will introduce the twisted topological K-theory and the associated twisted Atiyah-Hirzebruch spectral sequence, in which the TPIP fits nicely.
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报告人：古 星 博士（Max Planck Institute for Mathematics）
题 目：A Topological Approach to The Motivic Cohomology of BPGLn
时 间：2021.05.10（星期一），09:30-11:30
地 点：数学院南楼N224 腾讯会议：325 689 348
摘 要：For an algebraic group G over C, we have the classifying space BG in the sense of Totaro, which is an object in the unstable motivic homotopy category that plays a similar role in algebraic geometry as the classifying space of a Lie group in topology. The motivic cohomology (in particular, the Chow ring) of BG is closely related, via the cycle map, to the singular cohomology of the topological realization of BG, which is a classifying space in the usual sense. In this talk we exploit the above connection between motivic and singular cohomology to show that, at least in the case G = PGLn, we may study the Chow ring of BG through devices from algebraic topology, such as the Serre spectral sequences and the Steenrod operations.
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