# Hilbert's tenth problem

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Shilin Lai, Princeton University
Fine Hall 110

Hilbert's tenth problem asks for a process'' to decide if a Diophantine equation has integer solutions. This turned out to be impossible by the works of Davis--Putnam--Robinson and Matiyasevich. The talk will start with a basic introduction to computation theory, formalizing the notion of process''. It will then sketch the main ideas of the negative solution to Hilbert's tenth problem, which shows the much stronger conclusion that in some sense, Diophantine equations can simulate all computations.