Mathematics Department Colloquium

February 20
Russell Miller, CUNY
Computability on $\mathbb R$ and $\operatorname{Gal}(\mathbb Q)$

Traditionally, computability theory has been restricted to countable structures (such as groups or rings). We explain how digital computation by Turing machines can be applied to continuum-sized structures, with particular attention to the real numbers and the absolute Galois group of the rationals, and present some natural and intriguing questions regarding each.