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• Introduction to Deformation Theory

  Speaker: Shin Eui Song (UMD) - https://www.math.umd.edu/~sesong/
  

  When: Mon, October 4, 2021 - 5:00pm
  Where: Kirwan Hall 3206
  
• Moduli Space of Elliptic Curves

  Speaker: Samuel Bachhuber (UMD) -
  

  When: Mon, October 11, 2021 - 5:00pm
  Where: Kirwan Hall 3206
  
• Global moduli problems and representability

  Speaker: Jackson Hopper (UMD) -
  

  When: Mon, October 18, 2021 - 5:00pm
  Where: Kirwan Hall 3206
  
• Local deformation and Algebraization

  Speaker: Shin Eui Song (UMD) - https://www.math.umd.edu/~sesong
  

  When: Mon, October 25, 2021 - 5:00pm
  Where: Kirwan Hall 3206
  

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  Abstract: We first review local deformation functors. Studying local deformations is useful as there may not be any global moduli space. We will review the definition of versal deformations and effective formal deformation. One of the fascinating results is that having an effective formal versal deformation implies that an algebraization exists. This follows from a deep approximation theorem of Artin.
  
• The cotangent complex and applications to deformation theory

  Speaker: Steven Jin (UMD) -
  

  When: Mon, November 1, 2021 - 5:00pm
  Where: Kirwan Hall 3206
  

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  Abstract: Suppose $X$ is a scheme (or Artin stack) over a base scheme $S$. The cotangent complex of $X/S$ is a certain complex $L_{X/S}$ of locally free $\mathcal{O}_X$-modules in the nonpositive degrees that in some sense generalizes the sheaf of relative Kahler differentials. In this talk, we will motivate why such an object might be desirable, and we will sketch some of its most important properties. We will conclude with a discussion of how the cotangent complex controls the deformation theory of $X/S$.