Joint with Marco Schlichting. We show how to canonically derive an exact form category in the sense of Schlichting to a Poincaré category in the sense of the nine authors, and exhibit a natural equivalence between the Grothendieck-Witt spectra associated to each.
Joint with Yonatan Harpaz. We introduce a family of fibre-cofibre sequences, which we dub Keller sequences, in the category of exact \(\infty\)-categories generalising the notion of Verdier sequences of stable \(\infty\)-categories, and study their \(K\)-theoretic behaviour: we show that connective algebraic \(K\)-theory is Keller localising, and use this to give a categorical proof of the Gillet-Waldhausen theorem. We also give a self-contained proof of Waldhausen’s additivity theorem for exact \(\infty\)-categories. arXiv version.
This is a local, semistable version of my thesis, last updated May 2026.