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    Information, compact monoids and geometry
           Michael Mislove
          Tulane University

    Shannon's information theory describes the capacity of a channel over
    which symbols from an alphabet are sent. In this talk, I'll describe
    recent work that shows that compact monoids arise in the consideration
    of noise matrices for such channels, and how the structure of the
    monoid of noise matrices relates to the capacity of a channel. I'll
    include the necessary background from these areas, and I'll also
    describe how the theory can be generalized to alphabets that are
    infinite. It also reveals a relationship between this theory and the
    theory of labeled Markov processes, which are automata in which
    transitions are taken with certain probabilities. The work I'll
    describe relies on previous work of Martin, Moskowitz and Allwein [1]
    and is largely joint work with Keye Martin (NRL).

    [1] Martin, K., I. Moskowitz and G. Allwein, Algebraic information
    theory, Electronic Notes in Theoretical Computer Science 156 (2005),
    pp. 289-306.