Elia Mazzucchelli

Theoretical physicist — scattering amplitudes & positive geometry

I explore the geometric structures underlying scattering amplitudes, with a particular focus on their interpretation as volumes and on the structure of their singularities.

CV INSPIRE ORCID IAS profile
Portrait of Elia Mazzucchelli

Academic biography

Academic biography

I am a researcher working at the intersection of mathematics and theoretical physics, with a focus on scattering amplitudes and their underlying geometric and algebraic structures. I completed my master’s degree at ETH Zurich under the supervision of Matthias Gaberdiel, and my PhD at the Max Planck Institute for Physics in Munich under the supervision of Johannes Henn. From September 2026 to July 2029, I will be a Member in the School of Natural Sciences at the Institute for Advanced Study in Princeton.

Research

Some directions in amplitudes and geometry

Curved positive geometry, its dual region, and a measure supported on the dual.

Scattering amplitudes in planar 𝒩=4 super Yang–Mills theory can be encoded by positive geometries such as the amplituhedron, whose canonical differential form reproduces the amplitude or loop integrand. A central question is whether these canonical functions admit a dual interpretation as ordinary volumes. My work studies classes of positive geometries for which the canonical function can instead be represented as the volume of a probability distribution supported on a dual region. This makes positivity properties, including complete monotonicity, geometrically manifest and provides a new perspective on the dual amplituhedron problem.

Relevant papers: Canonical Forms as Dual Volumes Exterior Cyclic Polytopes and Convexity of Amplituhedra Positivity properties of scattering amplitudes

Line-incidence configurations for four lines in projective three-space.
Researchers illustrating configurations of lines in front of a blackboard.
Visualizing configurations of lines in projective three-space. From left to right: me, Ben Hollering, Bernd Sturmfels, Matteo Parisi.

In momentum twistors, propagators become incidences of lines in projective three-space. These conditions define algebraic varieties inside the Grassmannian of lines. My work uses tools from algebraic geometry, combinatorics, and computational geometry to study their equations, degrees, components, and real or positive loci. This creates a dictionary between geometric configurations of lines and the algebraic structures that appear in amplitude calculations.

Relevant papers: Varieties of Lines in 3-Space Hyperplane Arrangements in the Grassmannian Landau Analysis in the Grassmannian

Diagram from positive-geometry boundaries to Landau diagrams and Landau singularities.

The analytic structure of loop-level scattering amplitudes is encoded in their singularities. Positive geometry sharpens the usual Landau analysis by selecting only those boundary configurations that are compatible with the underlying geometry. Translating these boundaries into configurations of lines, and then into Landau diagrams, helps isolate the physically relevant algebraic solutions and provides an efficient route to determining symbol letters and leading singularities.

Relevant papers: Positivity and Cluster Structures in Landau Analysis Geometric Landau Analysis and Symbol Bootstrap All-loop Leading Singularities of Wilson Loops Landau Analysis in the Grassmannian

Selected work

A few papers I’m proud of

  1. Positivity and Cluster Structures in Landau Analysis

    Benjamin Hollering, Elia Mazzucchelli, Matteo Parisi, and Bernd Sturmfels · 2026-03-26 · arXiv preprint

    INSPIRE arXiv

  2. Varieties of Lines in 3-Space

    Benjamin Hollering, Elia Mazzucchelli, Matteo Parisi, and Bernd Sturmfels · 2025-11-26 · arXiv preprint

    INSPIRE arXiv

  3. Canonical Forms as Dual Volumes

    Elia Mazzucchelli and Prashanth Raman · 2025-09-02 · arXiv preprint

    INSPIRE arXiv

  4. Exterior Cyclic Polytopes and Convexity of Amplituhedra

    Elia Mazzucchelli and Elizabeth Pratt · 2025-07-23 · arXiv preprint

    INSPIRE arXiv

  5. All-loop Leading Singularities of Wilson Loops

    Taro V. Brown, Johannes M. Henn, Elia Mazzucchelli, and Jaroslav Trnka · 2025-03-21 · JHEP 06 (2026) 113

    INSPIRE arXiv
Full publication list on INSPIRE →

Selected talks

Recent and selected talks

  1. Positive Geometries as Dual Volumes

    Amplitudes and Algebraic Geometry · Erwin Schrödinger International Institute for Mathematics and Physics, Vienna · March 23, 2026

    Watch on YouTube

  2. From Amplituhedra to Exterior Cyclic Polytopes

    Graduate Online Combinatorics Colloquium (GOCC) · Online · December 10, 2025

    Watch on YouTube

  3. Positive Geometries and Canonical Forms

    Chow Lectures 2025 — Preparatory Lecture II · Max Planck Institute for Mathematics in the Sciences, Leipzig · October 6, 2025

    Watch on YouTube