🚀 Announcing geometric-langlands v0.1.0-alpha
We're excited to announce the first alpha release of geometric-langlands, a Rust implementation of computational methods for exploring the geometric Langlands conjecture!
📦 Installation
[dependencies]
geometric-langlands = "0.1.0"
🌟 Features
Mathematical Structures
- Reductive Groups: GL(n), SL(n), SO(n), Sp(2n) with complete algebraic structure
- Automorphic Forms: Eisenstein series, cusp forms, Hecke operators
- Galois Representations: Frobenius traces, L-functions, irreducibility testing
- Langlands Correspondence: Verification framework for the conjecture
Computational Tools
- L-Function Computation: Dirichlet series, functional equations, special values
- Neural Network Integration: Pattern learning for mathematical correspondences
- WASM Support: Run geometric Langlands computations in the browser
- Parallel Processing: Multi-threaded mathematical computations
Example Usage
use geometric_langlands::prelude::*;
// Create an automorphic form
let form = AutomorphicForm::eisenstein_series(2, 12);
// Compute Hecke eigenvalues
let hecke = HeckeOperator::new(2);
let eigenvalue = hecke.eigenvalue(&form)?;
// Verify Langlands correspondence
let langlands = LanglandsCorrespondence::new("GL(2)", "SL(2)");
let galois = langlands.automorphic_to_galois(&form)?;
let verified = langlands.verify_correspondence(&form, &galois)?;🧮 Mathematical Background
The geometric Langlands conjecture, recently proven by Gaitsgory-Raskin (2024), establishes a profound duality between:
- D-modules on moduli stacks of G-bundles
- Ind-coherent sheaves on stacks of local systems
This implementation provides computational tools to explore this correspondence.
📊 Current Status (v0.1.0-alpha)
✅ Implemented
- Core mathematical structures (40% complete)
- Basic Langlands correspondence verification
- Working examples and documentation
- WASM browser support
🚧 In Progress
- Advanced sheaf cohomology
- GPU acceleration (CUDA)
- Complete test coverage
- Neural network training
📚 Documentation
🤝 Contributing
This is an alpha release and we welcome contributions! Areas needing help:
- Mathematical validation
- Performance optimization
- Additional examples
- Documentation improvements
⚠️ Alpha Disclaimer
This is an early alpha release. While core functionality works, expect:
- API changes in future versions
- Incomplete features
- Performance improvements needed
- Documentation gaps
🔗 Links
🙏 Acknowledgments
Built on top of:
- nalgebra for linear algebra
- ndarray for tensor operations
- ruv-FANN for neural networks (planned integration)
Special thanks to the mathematical community for theoretical foundations.
Join us in making abstract mathematics computationally accessible! 🎉
🚀 Announcing geometric-langlands v0.1.0-alpha
We're excited to announce the first alpha release of geometric-langlands, a Rust implementation of computational methods for exploring the geometric Langlands conjecture!
📦 Installation
🌟 Features
Mathematical Structures
Computational Tools
Example Usage
🧮 Mathematical Background
The geometric Langlands conjecture, recently proven by Gaitsgory-Raskin (2024), establishes a profound duality between:
This implementation provides computational tools to explore this correspondence.
📊 Current Status (v0.1.0-alpha)
✅ Implemented
🚧 In Progress
📚 Documentation
🤝 Contributing
This is an alpha release and we welcome contributions! Areas needing help:
This is an early alpha release. While core functionality works, expect:
🔗 Links
🙏 Acknowledgments
Built on top of:
Special thanks to the mathematical community for theoretical foundations.
Join us in making abstract mathematics computationally accessible! 🎉