CYCluster

A database of Calabi–Yau differential operators

Search the AESZ database for arithmetic, algebraic, and enumerative information on Calabi–Yau operators, including Euler factors and monodromy structures.

Explore Calabi–Yau operators

Search the AESZ database of Calabi–Yau differential operators and explore the data associated with each record.

Search the operator database

About

The new AESZ database provides arithmetic, algebraic, and enumerative information that complements the list of one-parameter Calabi–Yau operators compiled by Gert Almkvist, Christian van Enckevort, Duco van Straten, and Wadim Zudilin [1, 2].

The main additions are Euler factors of the Hasse–Weil zeta function, calculated following [3] to identify rank-two attractor points and test Langlands-type conjectures. Further additions include rational and integral monodromy structures.

Supporting resources

Database API

Retrieve data for your own computations, with examples for Python, PARI/GP, and Mathematica.

Read the API guide

Bibliography

Find references on Calabi–Yau geometry, arithmetic, differential operators, and connections to physics.

Browse references

Latest updates

Note23 September 2026 — Homepage update

Operator search is now the main entry point on the homepage, with supporting links to API documentation and the bibliography. The event archive has been reorganized by date, with links to the original programmes.

Related databases and software

Resources for the study of Calabi–Yau and Fano varieties.

Databases

• Original AESZ database. The earlier database of Calabi–Yau differential operators.

• L-functions and Modular Forms Database (LMFDB). Data on L-functions, modular forms, and related arithmetic objects.

• Higher-genus invariants and Calabi–Yau data. Albrecht Klemm’s collection of data on Calabi–Yau threefolds and their enumerative invariants.

• Quantum periods of four-dimensional Fano varieties. Data from Tom Coates and Alexander M. Kasprzyk.

• Kreuzer–Skarke Calabi–Yau data. Max Kreuzer and Harald Skarke’s collections of 4,319 reflexive polytopes in dimension three and 473,800,776 in dimension four, including 30,108 distinct Hodge pairs for Calabi–Yau threefold hypersurface families.

Software tools

• CYTools. Software from the Liam McAllister Group for studying Calabi–Yau manifolds, including triangulations and intersection numbers.

• ore_algebra. Tools for analytic continuation of solutions of differential equations and computation of monodromy matrices.

Events archive

Past schools and workshops connected to the themes of CYCluster. Follow the event links for programme details and any materials made available by the organizers.

2025

Dates	Event	Location
17–28 November	Winter School on Number Theory and Physics	ICTP, Trieste
7–11 July	LuCANT	ICERM, Providence
7–11 July	Workshop on Explicit Arithmetic Geometry	ICTP, Trieste
30 June–4 July	School on Explicit Arithmetic Geometry	ICTP, Trieste
17–28 March	The Arithmetic of Calabi–Yau Manifolds	MITP, Mainz

2024

Dates	Event	Location
11–15 November	Murmurations in Arithmetic Geometry and Related Topics	Simons Center, Stony Brook
24–28 June	Workshop on Number Theory and Physics	ICTP, Trieste
17–21 June	School on Number Theory and Physics	ICTP, Trieste

Contribute

To contribute data or software, contact .

Spotted an issue?

Report a problem and follow its progress on the GitHub issue tracker. Please include the relevant page or operator identifier and, where applicable, the steps needed to reproduce the issue.

References

1.

Almkvist, G., Enckevort, C. van, Straten, D. van, Zudilin, W.: Tables of calabi–yau equations, https://arxiv.org/abs/math/0507430

2.

Straten, D. van: Calabi-Yau operators. In: Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds & Picard-Fuchs equations. pp. 401–451. Int. Press, Somerville, MA (2018)

3.

Candelas, P., Ossa, X. de la, Straten, D. van: Local zeta functions from calabi-yau differential equations, https://arxiv.org/abs/2104.07816