Define the object clearly
Mathematical notation should clarify the object being measured, not hide it.
Research
Questions before methods.
My work sits between mathematics, computation, and scientific data. I am interested in descriptions of structure that are mathematically clear, computationally practical, and interpretable in the scientific problem that motivated them.
How I work
Four principles guide the research.
The methods vary from project to project. These principles are more stable.
Keep interpretation close
A descriptor is more useful when its mathematical meaning can still be connected to structure.
Validate the computation
Implementation choices, numerical conventions, and reference checks are part of the scientific claim.
Match claims to evidence
Small data sets and exploratory analyses should lead to appropriately careful conclusions.
Current doctoral research
Bone structure and fragility
What structural information about trabecular bone is not captured by conventional summary measures?
Trabecular bone forms a network in three dimensions. Its mechanical behaviour depends on more than volume fraction, local thickness, or spacing. My current research studies whether topology, geometry, orientation, and graph structure can provide complementary descriptions.
Persistent homology tracks components, tunnels, and cavities across a filtration. Conventional morphometry and newer structural descriptors provide a second view of the same specimen. The modelling problem is then to ask what these different descriptions contribute when apparent strength is the outcome of interest.
Topology
Persistent homology of image intensity and signed distance filtrations.
Morphology
Thickness, separation, connectivity, anisotropy, orientation, skeleton, graph, and tensor descriptors.
Modelling
Careful regression and validation for a small cohort with measured mechanical outcomes.
Scientific computing
Computational morphology at scale
How can structural descriptors remain reviewable when the images become very large?
Open research software
bone_morphometry
A Rust program for region aware trabecular bone morphometry and the scalar descriptor families used in the associated strength analyses.
Large volume computation
Streaming topological summaries
Memory conscious methods for Betti and Minkowski summaries when a full image volume cannot be treated as one dense object in memory.
Topological data analysis
Ball Mapper and range queries
How much can the construction be accelerated without changing the mathematical object we intend to compute?
Ball Mapper gives a compact graph representation of data by constructing a cover with metric balls. My work separates that construction from the mechanism used to answer neighbourhood queries, which makes exact and approximate search strategies easier to study systematically.
The emphasis is not only speed. Boundary conventions, invariance, approximation behaviour, and reproducible experiments matter because they determine whether two implementations are computing the same mathematical construction.
Exact search
Clear distance and boundary conventions for reproducible cover construction.
Approximate search
Empirical study of faster neighbourhood queries and the changes they may introduce.
Software
Research direction
Topology in scientific machine learning
Can learned field models preserve structural information that matters to the underlying science?
Neural operators learn mappings between functions or fields. I am interested in whether topology can contribute useful structural information when the target is not a single scalar value but an entire physical field.
This direction connects the mathematical work on descriptors with mechanics and operator learning. The aim is to make topology part of the scientific representation, rather than adding it as a decorative regulariser after the model has already been designed.
Fields
Displacement, phase, rainfall, and other spatially varying quantities.
Structure
Topological summaries, local geometry, and descriptors that can be related to physical behaviour.
Learning
Operator models that map one field to another while preserving scientifically meaningful information.
Earlier work
Applications that shaped the current questions.
Earlier projects included topology informed ECG classification and computer vision for plastic pollution. They reinforced my preference for methods that remain connected to a concrete scientific or public problem.