Galaxy Morphology & Topological Representations
Persistent homology and self-supervised learning for robust, interpretable descriptors of galaxy images from surveys such as Galaxy Zoo.
Research
Research Themes
My research aims to connect algebraic topology and machine learning with concrete problems in astrophysics, complex systems, and condensed matter physics.
PhD project
My PhD focuses on Topological Data Analysis and Topological Deep Learning Applied to Physical Systems Across Scales. The central idea is to use persistent homology, Mapper, and graph neural networks to construct robust, interpretable descriptors of physical fields and time series.
- Goal: Build a unified framework where topological features can be systematically related to physical observables.
- Tools: Persistent homology, Betti curves, barcodes, Mapper graphs, GNNs, contrastive/self-supervised learning.
- Applications: Barkhausen noise, quantum information, condensed matter, MHD turbulence, dynamical systems, asteroseismology, gravitational waves, galaxy morphology.
Research Topics & Selected Works
A few representative topics I currently work on. Each card links to publications, talks, or software where you can find more details.
Gravitational Waves at Low SNR
Topological summaries of time-series data to detect gravitational-wave-like signals in very noisy regimes.
Asteroseismology & Stellar Structure
Using topological characteristics of oscillation spectra to study stellar structure and relate mode content to physical parameters.
Topological Diagnostics for MHD Simulations
Applying TDA to magnetohydrodynamic shock-tube simulations to understand the failure modes of convolutional neural network temporal predictors.
Complex Systems & Mapper Graphs
Using homology and Mapper to characterize phase-space structure in nonlinear dynamics and networked systems beyond pairwise interactions.
Barkhausen Noise & Disordered Media
Topological analysis of experimental Barkhausen noise and toy models to connect homological signatures with avalanche statistics and criticality.
Astronomical scale
At the astronomical scale, I study how topological signatures appear in data such as light curves, power spectra, and images. This includes:
- Topological descriptors of galaxy morphology from surveys such as Galaxy Zoo, combined with graph neural networks and self-supervised learning.
- Use of persistent homology and related tools to analyze gravitational-wave-like signals at low signal-to-noise ratios.
- TDA applied to asteroseismology, exploring the relation between mode spectra and homological features of frequency-domain representations.
- TDA-SSL Galaxy Morphology – Galaxy Zoo 2 + TDA + self-supervised learning.
- TDA for GW at low SNR – pipeline for robust detection using topological summaries.
Galaxy Zoo
Persistent homology
Contrastive learning
GNNs
Mesoscopic scale
At intermediate scales, my work explores fluid dynamics, magnetohydrodynamics, and dynamical systems. Topological tools are used to quantify structures such as shocks, vortices, and chaotic attractors.
- TDA diagnostics of CNN predictors on shock tube and other CFD test problems.
- Topology of trajectories in low-dimensional chaotic systems (e.g. Lorenz, Rössler, Chua).
- Connections between persistent homology and mixing / transport in MHD and turbulent flows.
- Shock tube benchmarks for ML-based solvers.
- Betti curves of attractors and their parameter dependence.
- Topological signatures of reconnection and field-line complexity.
MHD
Dynamical systems
Topological diagnostics
Microscopic scale
At small scales, I study how topological features emerge in magnetic materials, Barkhausen noise, and quantum systems.
- Persistent homology of Barkhausen voltage time series, relating topological invariants to domain-wall dynamics and scaling laws.
- TDA-inspired descriptors for phase transitions in lattice models and disordered media.
- Topological perspectives on entanglement and quantum state manifolds.
- TDA of experimental Barkhausen noise time series.
- Links between topological signatures and critical behaviour.
Barkhausen noise
Phase transitions
Quantum information