Giulio Salvatori

Theoretical physicist — scattering amplitudes & positive geometry

I look for the hidden geometry behind how particles scatter, reformulating quantum field theory in the language of curves on surfaces, polytopes, and tropical geometry.

Giulio Salvatori

Research

Curves, polytopes, and the shape of amplitudes

My work sits at the meeting point of scattering amplitudes, combinatorics, and geometry — the program sometimes called surfaceology. The recurring idea is that physical quantities are encoded by positive geometries: associahedra and their relatives, configuration spaces of curves on surfaces, and tropical limits that make hard integrals tractable. I'm also interested in the precision QCD side, computing master integrals for Higgs-plus-jet production at the LHC.

Scattering amplitudes Positive geometry Surfaceology Tropical geometry Feynman integrals Amplituhedra

Selected work

A few papers I'm proud of

SubTropica
with M. Giroux & S. Mizera · arXiv:2604.20954 · arXiv →
A Mathematica package for symbolic integration via tropical geometry.
All Loop Scattering as a Sampling Problem
single-authored · JHEP 02, 196 (2026) · arXiv →
The Tropical Geometry of Subtraction Schemes
single-authored · arXiv:2406.14606 · arXiv →
All Loop Scattering as a Counting Problem
with N. Arkani-Hamed, H. Frost, P-G. Plamondon et al. · JHEP 08, 194 (2025) · arXiv →
1-Loop Amplitudes from the Halohedron
single-authored · JHEP 2019, 74 (2019)

Full publication list on INSPIRE-HEP →

Demos

Things you can scroll

All demos →

Selected talks

Recent & favourite talks

All Loop Scattering as a Sampling Problem
Plenary · Amplitudes 2025, Seoul National University
A Primer on Surfaceology
Mathematical Physics Seminar, Perimeter Institute · 2025 · PIRSA →
Colorless Surfaceology
Plenary · QCD Meets Gravity 2024, NTU