Tools & Software

Open source software for rigorous signal processing and geometric analysis.

My research relies on building robust, mathematically rigorous tools. Below is a selection of open-source software I have developed or contributed to, ranging from high-performance signal processing infrastructure to formal proof assistants for mathematical physics.

Real-Time Infrastructure

The sgn Ecosystem

Core Developer

I contribute to the sgn framework, a next-generation ecosystem designed for the low-latency requirements of gravitational wave astronomy. My contributions focus on fundamental execution logic as well as detection-specific signal processing details.

  • sgn: Core library for real-time data processing, providing a modular architecture for building low-latency pipelines.
  • sgn-ts: A set of time-series extensions to the core sgn library, enabling efficient handling of streaming data and real-time data processing tasks.
  • sgn-ligo: A collection of LIGO-specific extensions to the sgn framework, including optimized implementations of matched filtering and other signal processing techniques tailored for gravitational wave detection.
  • sgnl: Detection pipeline and related utilities built on top of the sgn ecosystem, designed to facilitate the development and deployment of real-time detection algorithms. Inheriting conceptually from the GstLAL pipeline.

array-api-signal

Sole Developer – [Source]

A lightweight set of signal processing extensions built on the Array API standard. By leveraging the backend detection of array-api-compat, this library provides a unified interface for signal processing primitives (like window functions and filtering) that runs seamlessly on NumPy, PyTorch, or JAX. This library exists to extend the Array API to cover the specific needs of signal processing in gravitational wave astronomy, some of which are not yet covered by the core standard.

Geometry & Mathematical Physics

manifold

Core Developer – [Source]

A differential geometry library for constructing geometric template banks. By utilizing information geometry (specifically Fisher information metrics), manifold optimally places templates in high-dimensional parameter spaces. This ensures maximum physical coverage with minimal computational cost by treating the search space as a curved statistical manifold.

LoopGroup (Lean 4)

Sole Developer – [Source]

A formalization of Loop Groups (infinite-dimensional Lie groups) in the Lean 4 theorem prover. Currently under development, this project provides rigorous, computer-verified proofs for the algebraic structures underpinning gauge theory and integrable systems.

formality

Sole Developer – [Source]

A symbolic mathematics extension for sympy focused on combinatorics and finite group theory. Designed as a playground for algebraic experimentation, it provides specialized tools for manipulating Young Tableaux, generating Young Symmetrizer groups, and algorithmically searching for group isomorphisms to verify conjectures.

Specialized Utilities

zlw (Zero-Latency Whitening)

Sole Developer – [Source]

A specialized utility library for causal data whitening. Crucial for “Early Warning” detection systems, zlw characterizes noise power spectral densities in real-time without introducing non-causal artifacts (future data leakage), ensuring that analysis pipelines strictly respect the arrow of time.

sxolar

Sole Developer – [Source]

A lightweight, automated interface for the arXiv API. Designed to streamline literature reviews, it automates the tracking and filtering of new preprints in specific sub-fields of mathematical physics and geometry.

Pedagogical Resources

Interactive Signal Processing

Sole Developer

A suite of web-based interactive applications designed to visualize the core concepts of matched filtering and gravitational wave detection. These tools allow students and researchers to manipulate signal-to-noise ratios, visualize PSDs, and see real-time template matching in the browser.

  • DSP Filter Design Playground: See Related Note. An interactive tool for designing and visualizing digital filters, demonstrating the effects of different filter parameters on signal processing tasks, including poles and zeros, frequency response, stability, and causal vs non-causal filtering. Built with Dash and Plotly for an intuitive user experience. Source