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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### Machine learning Hilbert series

Neural networks find efficient ways to compute the Hilbert series, an important counting function in algebraic geometry and gauge theory.

### Calabi-Yau anomalies

Unsupervised machine-learning of the Hodge numbers of Calabi-Yau hypersurfaces detects new patterns with an unexpected linear dependence.

### 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.