A central or recurring theme in my work is Category Theory, in particular its applications to Algebraic Geometry and Homotopy Theory.

In more details, I am interested in higher algebra, which is, in a broad sense, the study of familiar algebraic structures—groups, rings, and others—suitably translated to (higher) categories.

Some instances where these gadgets concretely manifest themselves concern Intersection Theory and \(K\)-Theory, and the geometry of homotopy types. Here are some of the main themes:


  1. We should say ‘’banded,’’ using a rather ugly neologism.

  2. Or stacks, if we work over a site.

  3. It is known Waldhausen categories form a multi-category. So do Picard groupoids and their presentations.