Research
My research investigates how topological and geometric structure can be turned into interpretable observables for complex physical data, connecting persistent homology, machine learning, and scientific modeling from microscopic to astronomical scales.
My PhD focuses on Topological Data Analysis and Topological Deep Learning Applied to Physical Systems Across Scales. The central goal is to identify topological summaries that are not only statistically useful, but can also be related to physical mechanisms, observables, and changes of regime.
Three projects currently form the main multiscale backbone of my thesis, each asking how persistent topology can encode physically meaningful structure in a different class of data.
Topological observables of AGN variability
Multiband light curves of active galactic nuclei are studied through classical variability diagnostics, delay-space geometry, persistent homology, and multiscale statistics to characterize structure that is difficult to capture with single summary statistics.
Topology and geometry of behavioral learning
Movement trajectories from maze-learning and reversal tasks are analyzed using behavioral metrics, trajectory geometry, networks, information-theoretic quantities, and topological summaries to study how spatial organization changes during learning.
Persistent topology of quasiperiodic spectra
Persistent homology is applied to density-of-states representations of quasiperiodic systems and BCN monolayers, with emphasis on the relation between finite persistence features, spectral gaps, scaling, and physically interpretable spectral structure.
Beyond the three thesis anchors, I work on or actively explore the following directions across astrophysics, nonlinear dynamics, fluid and plasma physics, behavioral data, and condensed matter.
Topological, geometric, and multiscale descriptors of AGN variability and host-galaxy structure, with the goal of connecting morphology and temporal behavior to nuclear activity.
Persistent homology and representation learning for robust, interpretable descriptors of galaxy images, including unsupervised and self-supervised approaches.
Topological summaries of noisy gravitational-wave-like time series across signal-to-noise regimes, including sensitivity to physical parameters and robustness to noise.
Topological representations of oscillation spectra and stellar variability, seeking links between mode structure, stellar parameters, and multiscale geometric organization.
Delay embeddings, persistent homology, Mapper, and recurrence methods for nonlinear dynamics, attractors, transitions, and higher-order organization.
Statistical, geometric, network, and topological analysis of movement patterns during learning tasks, with emphasis on spatial strategies and behavioral transitions.
TDA and scientific machine learning for shocks, vortices, reconnection, turbulence, and the validation of data-driven predictors for fluid and plasma dynamics.
Persistent topology of avalanche-like signals and disordered systems, connecting homological signatures with statistics, criticality, and domain-wall dynamics.
Topological and Morse-theoretic approaches to changes of regime in lattice and statistical-mechanical models, with attention to critical behavior and order-parameter structure.
The recurring question is the same: which geometric or topological structures survive changes of representation, noise, resolution, and physical scale—and what do they mean physically?
AGN variability, stellar oscillations, galaxy morphology, gravitational-wave-like signals, and related inverse problems in astrophysics.
Nonlinear trajectories, learning dynamics, shocks, vortices, fluid and plasma simulations, and topology-aware diagnostics for scientific machine learning.
Quasiperiodic spectra, density of states, Barkhausen noise, disordered media, phase transitions, and topological structure in microscopic models.