Speaker: James Hunter (University of Wisconsin-Madison) Title: Higher-Order Reverse Topology Abstract: Reverse Mathematics studies equivalences between logical axioms and mathematical theorems. Traditional Reverse Mathematics is limited to subsystems of second-order arithmetic, and thus can consider only those mathematical theorems expressible in the language of second-order arithmetic. In a recent paper, Kohlenbach showed that Reverse Mathematics extends nicely to higher-order theories, and examined certain higher-order statements in mathematical analysis. The same techniques can be applied to statements about topological spaces of size continuum, allowing for an examination of statements more general than those studied by traditional Reverse Mathematics.