Research interests
My main area of research is my main area of research is Geometric Rigidity Theory: the study of how constraint systems – discretely-defined structures with geometric constraints between them – can be deformed.
As well as its uses for structural engineering, Geometric Rigidity Theory has some rather interesting applications. Some of these applications include:
Formation control for individual moving robots:
H-S. Ahn (2020). Formation control: Approaches for distributed agents. Springer Nature Switzerland AG. https://doi.org/10.1007/978-3-030-15187-4
Understanding structural properties of colloidal matter:
K. Liu, S. Henkes, and J.M. Schwarz (2019). Frictional rigidity percolation: A new universality class and its superuniversal connections through minimal rigidity proliferation. Physical Review X 9, 021006. https://doi.org/10.1103/PhysRevX.9.021006
Low-rank matrix completion problems:
A. Singer, M. Cucuringu (2010). Uniqueness of low-rank matrix completion by rigidity theory. SIAM Journal on Matrix Analysis and Applications 31:4, 1621–1641. https://doi.org/10.1137/090750688
Protein folding:
A. Sljoka (2022). Structural and functional analysis of proteins using rigidity theory. In: N. Katoh, et al. Sublinear Computation Paradigm. Springer, Singapore. https://doi.org/10.1007/978-981-16-4095-7_14
Maximum likelihood estimation for Gaussian graphical statistical models:
E. Gross, S. Sulivant (2018). The maximum likelihood threshold of a graph. Bernoulli 24:1, 386–407. https://doi.org/10.3150/16-BEJ881
Sensor network localisation:
Z. Zhu, A. Man-Cho So, Y. Ye (2010). Universal rigidity and edge sparsification for sensor network localization. SIAM Journal on Optimization 20:6, 3059–3081. https://doi.org/10.1137/090772009
Other topics I am interested in include Crystallography, Tiling Patterns, Tropical Geometry, Algebraic Statistics, Spectral Graph Theory, Convex Optimisation and Matroid Theory, as well as Discrete Geometry, Graph Theory and Combinatorics in general.