Department Colloquium

Abstract: On one hand, stable homotopy theory is a part of topology, concerning certain kinds of "asymptotic" questions where one allows a dimension to limit to infinity. On the other, it has quite an algebraic feel, and moreover has many precise connections to fundamental structures in pure algebra and arithmetic. I'll introduce some of these connections, involving the homotopy groups of spheres and algebraic K-theory, and I'll discuss how a succinct and general construction, called the "even filtration", provides a unifying framework that helps understand and generalize them.