Student Research

These activities have been supported by National Science Foundation Grant DMS-0400558

 

Project I: Computations of Lie algebra cohomology


  • An Introduction to Lie algebras and Lie algebra cohomology
  • Student programs for computing Lie algebra cohomology: this package contains four files created by students to compute Lie algebra cohomology
  • d1.txt: Magma code to create the first differential as a matrix for a given Lie algebra.
  • Matrix.java: a Java program to produce all higher differential matrices given the first differential.
  • toMagma.txt: Magma code which will input a matrix from a text file.  Magma commands can then be run on this matrix.
  • RemoveZero.java: a Java program to remove the zeros and columns from a matrix and track these removals.  The purpose is to create a matrix smaller in size that could then be read in to Magma.
  • The Magma homepage
  • Some Computations of Lie algebra cohomology groups

Project II: Vanishing of line bundle cohomology


This work is based on the theory and program developed by Anne Lund Christophersen in her Aarhus University Ph.D. Thesis.


If you have difficulty accessing/using any of these files or want the original java files, please contact Chris Bendel.