Prof. Heather Harrington

Status

Academic Faculty
Royal Society University Research Fellow

Research interests

Applied algebra, chemical reaction network theory, mathematical modeling, topological data analysis, systems biology

• Brain chains as topological signatures for Alzheimer’s disease
  Goodbrake, C Beers, D Thompson, T Harrington, H Goriely, A Journal of Applied and Computational Topology (26 Apr 2024)
• Barcodes distinguishing morphology of neuronal tauopathy
  Beers, D Goniotaki, D Hanger, D Goriely, A Harrington, H Physical Review Research volume 5 issue 4 043006 (04 Oct 2023)
• Zigzag persistence for coral reef resilience using a stochastic spatial model.
  McDonald, R Neuhausler, R Robinson, M Larsen, L Harrington, H Bruna, M Journal of the Royal Society, Interface volume 20 issue 205 20230280 (23 Aug 2023)
• Homology of homologous knotted proteins
  Benjamin, K Mukta, L Moryoussef, G Uren, C Harrington, H Tillmann, U Barbensi, A Journal of the Royal Society Interface volume 20 issue 201 (26 Apr 2023)
• Dynamics on networks with higher-order interactions.
  Gao, Z Ghosh, D Harrington, H Restrepo, J Taylor, D Chaos (Woodbury, N.Y.) volume 33 issue 4 040401 (Apr 2023)

• Philip Leverhulme Prize 2020
• Adams Prize 2019
• LMS Whitehead Prize 2018
• Royal Society URF 2017-2022
• EPSRC Postdoctoral Fellowship 2014-2017
• Hooke Research Fellowship 2013-2014
• NSF Graduate Fellowship 2007-2010
• Barry M Goldwater Scholarship 2005-2006

Heather Harrington

ABSTRACT

Application driven topological data analysis

Persistent homology (PH) is a central tool in topological data analysis. PH provides a multiscale geometric descriptor of data that is functorial, stable to perturbations and interpretable, leading to many applications in mathematics and real-world data. Frequently one starts with point cloud data, a finite subset of a metric space (eg Euclidean space) and studies the topology arising from a filtration of simplicial complexes built on the data. While this process yields an interesting nontrivial descriptor of the "shape of data", some theoretical questions remain.

In this talk, we will present two directions in application-driven point cloud persistence. First, we will focus on the spaces of point clouds with the same persistence. This inverse problem asks the following: What is the shape of the fiber of the persistent homology map? The second problem is motivated by spatial data arising in biology, which includes outliers (eg histology) or dynamic metric spaces (eg collective dynamics). We present statistics for multiparameter persistence and then apply it to complex biological data. To study these two PH directions, we adapt tools from applied and computational algebraic geometry.

Saul Schleimer received his PhD from the University of California at Berkeley.

Since 2007 he has lectured at the University of Warwick, where he is currently an Associate Professor. Schleimer is a geometric topologist. His other interests include combinatorial group theory and computation.

He is especially interested in the visualisation of ideas from these fields. To promote such work, and outreach more generally, he co-founded the Illustrating Mathematics illustratingmath.org Steering Committee in 2022.

Saul Schleimer

ABSTRACT

PUZZLING THE 120-CELL

Interlocking puzzles (also called burr puzzles) are a great way to challenge your eyes, hands, and brain. You have to use both logic and spatial senses to figure out how the pieces fit together. In this talk, we'll use our understanding of four-dimensional space to build "Quintessence", a new family of 3D-printed interlocking puzzles.

These are based on the geometry and combinatorics of the 120-cell. After giving some mathematical background, I'll explain the construction of the puzzles. There will be many, many pictures. At the end of the talk the audience will be invited to solve some of the puzzles.