Here you can find information about talks I have given.
The Euler characteristic is an invariant of manifolds which is preserved under an equivalence relation called bordism. The set of bordism classes of manifolds admits a commutative ring structure, and this invariant lifts to a ring homomorphism. In fact, bordism defines a homology theory, and gives rise to a topological object called a ring spectrum. In this talk, I will discuss the problem of lifting the Euler characteristic ring homomorphism to a map of ring spectra, and the various difficulties involved when considering commutativity.