Sunday, September 26, 2004

Extensions

  • Consider talking in the algebra seminar about the theorem that inspired the results in my dissertation.
  • Consider picking up work on extending said theorem from the case of "over a field k" to "over a commutative integral domain K." However, original theorem relies on noetherian algebras being generically flat (not free, but flat) over dedekind domains. No idea how to take the part where things are automatic for k[t] and make them work for K[t].
  • Contemplate poking around in the arxiv and on MathSciNet and on relevent people's web pages (students of original authors comes to mind as a good place to start) to see if any of them have figured this out in the intervening five or so years that I've been mulling this problem over with no progress.
  • Ponder the wisdom of resuming work of applying results and techniques of dissertation to solving another special case of a 60-year-old unsolved problem.
  • Wonder how to find something else to work on without talking to Advisor.
  • Try reading more of Hopf Algebra book in hopes of understanding enough about Quantum Groups to try to relate own insular knowledge to things that other people are doing.
  • Check on crank.net to see if all the problems have been solved or if all of math has been disproved.