Gabriel Wendell

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/complex systems, neurosicence of learning, asteroseismology, gravitational waves, galaxy morphology, active galaxy nuclei.

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.

Mosaic of galaxy images illustrating different morphologies.

Active Galaxy Nuclei

Combining topological descriptors of AGN host galaxies with multifractal analysis to study the connection between morphology and nuclear activity in large surveys.

Mosaic of galaxy images illustrating different morphologies.

Galaxy Morphology Classification

Persistent homology and self-supervised learning for robust, interpretable descriptors of galaxy images from surveys such as Galaxy Zoo.

Time series and spectrogram of gravitational-wave-like data.

Gravitational Waves Detection

Topological summaries of noisy time-series simulated data based on gravitational-wave searches at high and low SNR ratios, exploring their relation to physical parameters.

Oscillation spectrum representing asteroseismology data.

Asteroseismology of Solar-like Stars

Combining asteroseismic analysis with topological characteristics of oscillation spectra to study stellar structure and relate mode content to physical parameters.

Network representation illustrating complex systems.

Dynamical Systems & Complex Systems

Using homology and Mapper to characterize phase-space structure in nonlinear dynamics and networked systems beyond pairwise interactions.

Neuroscience illustration.

Neuroscience of Learning

Statistical and topological analysis of movement patterns during learning tasks, relating homological features to cognitive processes and behavioral performance.

Magnetohydrodynamic shock-tube simulation.

(Magneto)hydrodynamic Simulations

Applying TDA to (magneto)hydrodynamic simulations to study the topology of shocks, vortices, reconnection sites, and turbulent flows.

Avalanche distribution reminiscent of Barkhausen noise.

Barkhausen Noise & Disordered Media

Topological analysis of experimental Barkhausen noise data and toy models to connect homological signatures with avalanche statistics and criticality.

Avalanche distribution reminiscent of Barkhausen noise.

Magnetic Phase Transitions

Using TDA-inspired descriptors to study phase transitions in lattice models and disordered media, relating topological signatures to critical behaviour and universality classes.

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.
Ongoing work
  • 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.
Ongoing work
  • 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.
Ongoing work
  • TDA of experimental Barkhausen noise time series.
  • Links between topological signatures and critical behaviour.
Barkhausen noise Phase transitions Quantum information