Research

My research is in geometry and topology and their applications to data science. My research focuses on topological data analysis (TDA), optimal transport and mathematical approaches to data science in general. I am particularly interested in applications to geospatial data analysis, redistricting and election reform. I am also interested in coarse geometry – the study of large scale properties of metric spaces – which has strong mathematical connections to geometric group theory, functional analysis and the topology of manifolds.

Some recent papers/preprints

Measuring segregation via analysis on graphs (w/ Moon Duchin and James Murphy)

Coarse embeddings of quotients by finite group actions via the sliced Wasserstein distance

Coarse embeddability of Wasserstein space and the space of persistence diagrams (w/ Neil Pritchard)

Topological analysis of U.S. city demographics (w/ Jakini Kauba)

Published papers

T Needham and T Weighill, Geometric averages of partitioned datasets, SIAM Journal on Applied Algebra and Geometry 7.1, 2023.
H Akitaya, A Gonczi, D Souvaine, C Toth, T Weighill, Reconfiguration of Polygonal Subdivisions via Recombination, 31st Annual European Symposium on Algorithms, 2023.
S Byers, N Pritchard, J Turner and T Weighill, Detecting spatial dependence with persistent homology, Nonlinear Theory and Its Applications, IEICE 14.2 (2023): 106-125.
M Duchin, J Murphy and T Weighill, Measuring segregation via analysis on graphs, SIAM Journal on Matrix Analysis and Applications 44.1 (2023): 80-105.
T Weighill, T Yamauchi, and N Zava, Coarse infinite-dimensionality of hyperspaces of finite subsets, European Journal of Mathematics 8.1 (2022): 335-355.
M Duchin, T Needham, and T Weighill. The (homological) persistence of gerrymandering. Foundations of Data Science 4.4 (2022): 581-622.
T Weighill, Lifting coarse homotopies, Advances in Geometry 21.4 (2021): 577-590.
T Abrishami, N Guillen, P Rule, Z Schutzman, J Solomon, T Weighill and Si Wu, Geometry of Graph Partitions via Optimal Transport, SIAM Journal on Scientific Computing 42.5 (2020): A3340-A3366.
L Higginbotham and T Weighill, Coarse quotients by group actions and the maximal Roe algebra, Journal of Topology and Analysis 11.04, 2019, 875-907.
J Dydak and T Weighill, Monotone-light factorizations in coarse geometry, Topology Appl. 239, 2018, 160-180.
J Dydak and T Weighill, Extension theorems for large scale spaces via coarse neighbourhoods, Mediterranean Journal of Mathematics 15, 2018, 59.
T Weighill, Mal’tsev objects, $R_1$-spaces and ultrametric spaces, Theory and Applications of Categories 32, 1485-1500, 2017.
T Weighill, On spaces with connected Higson coronas, Topology Appl. 209, 2016, 301-315.
Z Janelidze and T Weighill, Duality in non-abelian algebra III. Normal categories and 0-regular varieties, Algebra Universalis 77, 2017, 1-28.
Z Janelidze and T Weighill, Duality in non-abelian algebra II. From Isbell bicategories to Grandis exact categories, J. Homotopy Relat. Struct. 11, 2016, 553-570.
Z Janelidze and T Weighill, Duality in non-abelian algebra I. From cover relations to Grandis ex2-categories, Theory and Applications of Categories 29.11, 2014, 315-331.