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:姜清元(Universigy of Edinburgh
  目:Non-abelian Derived Categories and Derived Schur and Weyl Functors
  间:2023.04.03(星期一),16:30-17:30
  点:腾讯会议:377-9935-3697

  要:We'll start with reviewing Quillen and Lurie's theory of non-abelian derived categories (also known as the "animation" theory). Following that, we will apply this theory to generalize the classical Schur and Weyl functors of GL_n-representation theory to the cases of connective complexes, and investigate their fundamental properties. If time allows, we will also talk about how to generalize them to non-connective cases using Goodwillies theory of calculus of functors. 

Based on the first part of the paper arXiv:2212.10488.
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报告人:姜清元(Universigy of Edinburgh
  目:BorelWeiBott theorem for Derived Flag Schemes
  间:2023.04.04(星期二),16:30-17:30
  点:腾讯会议:377-9935-3697

  要:The framework of derived algebraic geometry (DAG), developed by Toen-Vezzosi, Lurie and many others, allows us to extend Grothendiecks theory of flag schemes of sheaves to the cases of complexes. In the first half of the talk, we will define and study flag schemes of complexes using DAG.

The BorelWeilBott theorem provides a fundamental link between algebraic geometry and representation theory. In the second half of the talk, we will establish a derived generalization of the BorelWeiBott theorem for flag schemes of [-1,0]-perfect complexes. 

Based on the second part of the paper arXiv:2212.10488.

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