Inaugural Lecture: Geometric Data Science - Prof Vitaliy Kurlin
Elizabath Gidney Room - University of Liverpool Guild of Students, Liverpool, L3 5TR
Tuesday 26th May 2026
Please join us for the Inaugural Lecture for Professor Vitaliy Kurlin of the School of Computer Science and Informatics.
Lecture in Guild of Students, Elizabeth Gidney room (Followed by Networking Drinks Reception)
Title: Geometric Data Science
The emerging area of Geometric Data Science studies real data objects under practical equivalences
[1]. The key example is a point cloud under isometry or rigid motion. In a Euclidean space, if given points are ordered, their isometry class is uniquely determined by the matrix of pairwise distances. A naive extension to m unordered points requires exponentially many matrices depending on m! permutations. The case of m=3 points was settled 2000+ years ago due to the side-side-side theorem from school geometry. However, even for m=4 points in the plane, there are infinitely many 4-point clouds that are indistinguishable by 6 pairwise distances.
The talk will describe a simple invariant that finished the case of 4 points [2] and a complete invariant with Lipschitz continuous metrics that resolved the exponential challenge in polynomial time in the number of points for any fixed Euclidean dimension [3].
[1] O.Anosova, V.Kurlin. Geometric Data Science book (arxiv.org:2512.05040), the latest version at https://kurlin.org/Geometric-Data-Science-book.pdf
[2] D.Widdowson, V.Kurlin. Resolving the data ambiguity for periodic crystals.NeurIPS 2022, v.35, p.24625-24638. Extended version to appear in SIAM J Applied Mathematics, arxiv:2108.04798.
[3] D.Widdowson, V.Kurlin. Recognizing rigid patterns of unlabeled point clouds by complete and continuous isometry invariants with no false negatives and no false positives. Proceedings of CVPR 2023, p.1275-1284. Extended at arxiv:2303.14161 and arxiv:2303.13486.
Lecture in Guild of Students, Elizabeth Gidney room (Followed by Networking Drinks Reception)
Title: Geometric Data Science
The emerging area of Geometric Data Science studies real data objects under practical equivalences
[1]. The key example is a point cloud under isometry or rigid motion. In a Euclidean space, if given points are ordered, their isometry class is uniquely determined by the matrix of pairwise distances. A naive extension to m unordered points requires exponentially many matrices depending on m! permutations. The case of m=3 points was settled 2000+ years ago due to the side-side-side theorem from school geometry. However, even for m=4 points in the plane, there are infinitely many 4-point clouds that are indistinguishable by 6 pairwise distances.
The talk will describe a simple invariant that finished the case of 4 points [2] and a complete invariant with Lipschitz continuous metrics that resolved the exponential challenge in polynomial time in the number of points for any fixed Euclidean dimension [3].
[1] O.Anosova, V.Kurlin. Geometric Data Science book (arxiv.org:2512.05040), the latest version at https://kurlin.org/Geometric-Data-Science-book.pdf
[2] D.Widdowson, V.Kurlin. Resolving the data ambiguity for periodic crystals.NeurIPS 2022, v.35, p.24625-24638. Extended version to appear in SIAM J Applied Mathematics, arxiv:2108.04798.
[3] D.Widdowson, V.Kurlin. Recognizing rigid patterns of unlabeled point clouds by complete and continuous isometry invariants with no false negatives and no false positives. Proceedings of CVPR 2023, p.1275-1284. Extended at arxiv:2303.14161 and arxiv:2303.13486.
