John Roberts was born in England, but his father came from the Llŷn Peninsula. He worked in Rome at Tor Vergata for a long time, before living his last few years in Goettingen.
John Roberts wrote his PhD thesis was on rigged Hilbert spaces, a way of making Dirac’s description of quantum mechanics precise. After that he followed the Haag-Kastler approach for axiomatizing quantum theory and became one of its central proponents.
Early on he suggested in
that local nets of observables should carry a notion of cohomology – or rather of nonabelian cohomology – with coefficients in an ∞-category. Motivated by this he was one of the first to consider strict ω-categories. He conjectured that these are characterized by their ω-nerves being complicial sets. This led Ross Street to develop the notion of orientals and eventually to prove this conjecture. An account of this development is on pages 9-10 of
Later Roberts proved together with Doplicher what is now one of the central results in AQFT, the Doplicher-Roberts reconstruction theorem – a version of Tannaka duality – which in the context of AQFT serves to intrinsically characterize the superselection sectors of a QFT. See also DHR superselection theory.