Computability Theory and The Solution of Hilbert's Tenth Problem -- Tony Capra, April 2, 2002

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In this talk I will introduce Hilbert's Tenth Problem, to determine the 
existence a universal algorithm for solving Diophantine equations, and use 
it as a motivation to investigate some basic results in the theory of 
computation. First I will develop a rigorous notion of computation through 
models such as the Turing machine and Church's lambda calculus. Then I will 
look at the "Entscheidungsproblem" and the notions of decidability and 
enumerability. Finally, using some of the concepts introduced in this talk, 
I will sketch Matijasevich's solution of Hilbert's Tenth Problem.