BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Carolina Figueiredo (Princeton) DTSTART:20260127T193000Z DTEND:20260127T203000Z DTSTAMP:20260423T005712Z UID:nhetc/127 DESCRIPTION:Title: Large $n$: scattering amplitudes at large multiplicity\nby Carolina Fi gueiredo (Princeton) as part of NHETC Seminar\n\n\nAbstract\nWhat happens when we scatter a large number $n$ of particles\, say with $n = 10^1000$? This question is out of reach of all existing approaches to scattering amp litudes\, whether directly through Feynman diagrams or recursion relations . In this talk\, I will study this problem at tree-level for a simple scal ar theory\, Tr($\\phi^3$) theory\, and describe a new way of accessing thi s regime\, starting from the "tropical" representation of the amplitudes g iven by the formalism of surfaceology. Remarkably\, we find that at large $n$ the sum over diagrams "smooths out". Working at leading order in $n$\ , and in certain "positive" regions of kinematic space\, the final answer is astonishingly simple\, given by a single term\, determined by an optimi zation problem associated with a biased random walk. I will also describe a transformation from the tropical representation to a new "dual" theory f or amplitudes\, which in simple limits reduces to the motion of a particle on a half-line\, evolving for a "time'' $n$\, allowing us to systematical ly extract the $1/n$ expansion of the amplitude. I will end by explaining how these results generalize to other large $n$ contexts\, from the scatte ring of pions\, to string scattering at ultra-high energies.\n LOCATION:https://researchseminars.org/talk/nhetc/127/ END:VEVENT END:VCALENDAR