Computational Topology Group - University of Edinburgh

About

We study the algebraic and computational structure of topological spaces, with particular emphasis on persistent homology, sheaf theory, and applied topology. Our work spans pure mathematics, algorithm design, and applications to data science and materials science.

The group was founded in 2019 and currently comprises 3 faculty, 4 postdocs, and 7 PhD students.

People

Prof. Signe Kolmogorov Group Lead · Chair of Computational Topology

Persistent homology, topological data analysis, sheaf cohomology. Previously at ETH Zürich and the Max Planck Institute for Mathematics.

Dr. Tomasz Nowak Lecturer

Discrete Morse theory, simplicial complexes, computational geometry. Interested in efficient algorithms for topological invariants.

Dr. Amira Lakhdari Postdoctoral Researcher (EPSRC Fellowship)

Mapper algorithms, multi-parameter persistence, applications to neuroscience data. PhD from Paris-Saclay, 2023.

Internal: Staffing Notes

Tomasz’s contract renewal due April 2026 — strong case, begin paperwork in Feb
Amira interviewing at Cambridge (Peterhouse fellowship) — consider retention package
PhD recruitment: 12 applications received for 2 funded positions. Shortlist meeting Feb 14.
Budget reallocation: £8,400 from travel fund to equipment (cluster GPU nodes)

Selected Publications

Stability of Multi-Parameter Persistence Modules under Noise

S. Kolmogorov, A. Lakhdari, J. Chen · J. Applied Topology, 2025

Efficient Computation of Persistent Homology via Discrete Morse Reduction

T. Nowak, S. Kolmogorov · SIAM J. Computing, 2024

Sheaf-Theoretic Approaches to Sensor Network Coverage

A. Lakhdari, M. Robinson · arXiv:2601.04821

Internal: Unpublished Drafts & Works in Progress

On the Homotopy Type of Configuration Spaces of Metric Graphs

S. Kolmogorov, T. Nowak · Draft - do not circulate

Contains the new spectral sequence argument. Key result: Theorem 4.7 gives a complete characterization for trees. Reviewer 2 concerns addressed in v3.

Persistent Homology of Financial Time Series: A Cautionary Tale

A. Lakhdari, E. Voss · Draft - submitted to NeurIPS 2026

Negative result. Shows that several published TDA-finance results fail to replicate. Controversial — Signe suggests we wait for reviews before any talks.

Internal: Grant Portfolio

Grant	Funder	Amount	Period	Status
Topological Methods in Materials Science	EPSRC	£842,000	2024–2028	Active
Computational Sheaf Theory	Leverhulme Trust	£195,000	2025–2027	Active
TDA for Neuroscience	Wellcome Trust	£310,000	2025–2028	Active
Persistent Homology at Scale	EPSRC	£520,000	2026–2029	Pending

Total active funding: £1,347,000. Overhead rate: 48%. PI discretionary: £24,600 remaining.

Contact

James Clerk Maxwell Building, Room 5325
University of Edinburgh
Peter Guthrie Tait Road
Edinburgh EH9 3FD

General enquiries: comptop@ed.ac.uk