URegina Topology and Geometry Seminar: Yang Hu

A ring spectrum (a.k.a. a multiplicative cohomology theory) $E$is complex-orientable if every complex vector bundle admits a Thom class in $E$. While many familiar spectra are complex-orientable, notable examples fail to be so — such as real K-theory and topological modular forms. To measure this failure precisely, two competing ideas have been proposed: the complex orientation order and the chromatic defect. A natural question is whether the two notions are related. In this talk, we will present examples that suggest a negative answer. This is joint work with Prasit Bhattacharya and Christian Carrick.