Photo of Dr Vitaliy Kurlin

Dr Vitaliy Kurlin PhD

Senior Lecturer (Associate Professor) Computer Science


Topological Data Analysis

TDA and related areas
TDA and related areas

Topological Data Analysis (TDA) provides stable-under-noise methods to quantify geometric properties of topological features such as cycles and holes in unorganised data across all scales. Our group also develops TDA applications to Materials Science (with Materials Innovation Factory at Liverpool and Cambridge Crystallographic Data Centre, UK), Computer Vision (with Microsoft Research at Cambridge, UK), Climate (with the Intel Parallel Computing Centre at the University of Liverpool and Lawrence Berkeley National laboratory, USA). More details including papers, C++ software and blog are on the personal webpage

Mathematical crystallography

Our Topological Data Analysis group develops a new continuous approach to quantify a similarity of solid crystalline materials. The new methods go beyond the past discrete classifications in terms of symmetry groups in order to quickly analyse large datasets of simulated crystals for more efficient crystal structure prediction.

Pure mathematics

Topology (embeddings of graphs and high-dimensional knots), singularities (1-parameter projections of links), non-commutative algebra (exponential equations and braid groups)

Research Grants

Application-driven Topological Data Analysis


September 2018 - August 2023

Topological Data Analysis for Faster Materials Discovery


December 2017 - December 2019

Topological analysis of climate systems


April 2017 - April 2020

Research Collaborations


Project: Group Leader
External: Lawrence Berkeley National laboratory, US

Topological Analysis of Climate Data

Andrew Fitzgibbon

Project: Principal Researcher
External: Microsoft Research Cambridge

Resolution-independent superpixels