Our papers are the official record of our discoveries. They allow others to build on and apply our work. Each paper is the result of many months of research, so we make a special effort to make them clear, beautiful and inspirational, and publish them in leading journals.

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Algebraic geometry

### Bundled Laplacians

By approximating the basis of eigenfunctions, we computationally determine the harmonic modes of bundle-valued Laplacians on Calabi-Yau manifolds.

General relativity

### Absorption with amplitudes

How gravitational waves are absorbed by a black hole is understood, for the first time, through effective on-shell scattering amplitudes.

quantum field theory

### Peculiar betas

The beta function for a class of sigma models is not found to be geometric, but rather has an elegant form in the context of algebraic data.

String theory

### Gauge theory and integrability

The algebra of a toric quiver gauge theory recovers the Bethe ansatz, revealing the relation between gauge theories and integrable systems.

String theory

### Algebra of melting crystals

Certain states in quantum field theories are described by the geometry and algebra of melting crystals via properties of partition functions.

String theory

### QFT and kids’ drawings

Groethendieck's “children’s drawings”, a type of bipartite graph, link number theory, geometry, and the physics of conformal field theory.