This is a continuation of my conference coverage from last week. The same warnings apply: this is much more technical than my usual posts, readers beware!

Last week I covered the talks from Monday through Wednesday, so I’ll jump right in here with Thursday morning, where the first speaker was Francesco Riva, who after a brief ad for his new board game Tutti Quantum gave a review of positivity constraints, first-principles restrictions on quantum field theories based on their behavior at high energies. After covering some of the research program’s successes like arguments against Galileons and massive gravity, he talked about how new methods allow one to take into account the possibility of loops of massless particles, essentially by invoking a formal version of the idea that real experiments have finite size. He was followed by Grant Remmen, who talked about his work deriving string theory-like amplitudes from increasingly minimal assumptions. While one can always quibble with the assumptions they impose, I do find it encouraging that they are now managing to do this game with both gravity and gauge theory, and with five-particle amplitudes, not just four.

Paul Heslop then covered applications of bootstrap techniques to non-supersymmetric theories, where analytic superspace still finds a way to be useful. Tomasz Taylor covered progress in calculating Yang-Mills amplitudes in de Sitter space. Andrea Puhm and Nima Arkani-Hamed don’t have slides online yet: Puhm’s title suggests her talk was part of the celestial holography field, while Nima’s was likely similar to his talk at Lancefest, where he talked about calculations of amplitudes in the limit of a very large number of loops (represented in the field with a capital L) or very large numbers of particles (represented in the field with a lower-case n). Given the different context, I’m guessing he left out the self-effacing jokes where he was “little n” and Lance was “big L”, though I’m hoping he at least mentioned his students had been checking their results against what they called the “lanswer”.

The evening ended with a gong show, which for the non-initiated is a series of short student talks with a strict time limit (hence the gong). I’m not quite so intrepid as to read all of the slides for these, commenters who attended are welcome to highlight special examples.

Friday began with a talk by Agnese Bissi, who reviewed the connection between holographic correlators and amplitudes in AdS space. I liked her emphasis on this as a lab to find nice new representations of amplitudes, and her summary at the end of the current frontiers. Axel Kleinschmidt followed with a talk on one-loop string amplitudes, where he and his collaborators have gotten gradually more proficient at manipulating the rich structure of elliptic functions that make an appearance. Piotr Tourkine talked about his work using the S-matrix bootstrap to find scattering amplitudes in higher dimensions, a context where accounting for thresholds presented a new challenge. This is a problem people are approaching with genuine supercomputers, he quoted one calculation at 100,000 CPU hours. Lauren Williams is one of a small community of mathematicians who have been intrigued by the amplituhedron, her talk was a walk through a series of conjectures, some made by physicists, some by mathematicians, most with counterexamples found in the last few years.

Finally, Zvi Bern closed the conference with a talk on the frontier of amplitudes-based gravitational wave calculations, referring to it, probably to David Kosower’s annoyance, as 5PM. Some parts of this frontier have been calculated, but a few have proved hard going, bottlenecked by immensely challenging integrals, which go beyond the capabilities of publicly available codes. The new integrals have a variety of strange functions, including the elliptics and Calabi-Yaus I spent time on in my own career, as well as Heun integrals, which I imagine I will have to learn more about from the slides of Elliptics & beyond ’26, as I don’t remember people talking about them when I was in the field. New integration strategies have led to improvements in the public codes and seem to be making good progress, but Zvi highlighted that ideally they want to not need supercomputers at all, as they’ll need to go higher in loops to see effects from, for example, the deformability of neutron stars.

Amplitudes 2027 will be in Munich, with the summer school in Mainz under Stefan Weinzierl’s capable hands. I’m looking forward to seeing what the state of the art looks like then!