Cycling in Cambridge

I spent most of my time here cycling (or is it biking?) and thinking about algebraic cycles from a homotopical viewpoint. I will speak about the latter. In joint work with Matthew Morrow, we developed a theory of motivic cohomology of schemes beyond the case of smooth schemes over a field. I will explain the cycle-theoretic aspects of this construction, focusing on the case of surfaces, revisiting older results of Krishna and Srinivas.