Based on: Stable and Unstable Operations in mod p Cohomology Theories.

One of the pieces of baggage that comes with a graded cohomology theory is the family of operations. These are self-maps of the cohomology groups obeying certain obvious naturality conditions. There are two main types of operation: stable and unstable. An unstable operation acts only on the cohomology groups of a particular degree whilst a stable operation acts on the cohomology groups of any degree compatibly with the suspension isomorphism. It is clear, therefore, that a stable operation defines a family of unstable ones. However, even if one knows that an unstable operation came from a stable one it may not be easy to reconstruct that stable operation. What is remarkable about the Morava K-theories is that there is a straightforward way to do this.

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This talk was given as a computer presentation, created using the LaTeX-Beamer class. I learnt Beamer and wrote the presentation in a short space of time. After given the presentation, seeing some other talks given using Beamer, and reading the user guide in full, I decided that I would have done some things a little differently. These were all stylistic or coding changes: I have not changed the individual slides or their order. If you just want an idea of what the talk was about, take a look at the "New and Improved Version (short)". This is the transparency version where the frames are shown in full with none of the more dynamic effects.

• Original slides in pdf, and the LaTeX source.
  
• New and Improved Version in pdf (short), pdf (long), LaTeX source.