About me
I am a Lecturer in Mathematics at St Andrews.
I like to work on problems that feature an interaction between geometry, combinatorics, and algorithmic considerations. I also like theoretical problems that arise out of concrete, applied scenarios.
I’m interested in discrete geometry generally, and the rigidity and flexibility of frameworks specifically, with connections to applications in physics, materials, and machine learning.
For more detail, see the list of publications below, the short overview or my full CV. To find me, see my contact information.
Research
My research papers by type in approximate reverse chronological order. click on the titles to see abstracts and get the full text. You can also see a list of my coauthors. Jump to: journal papers; conference papers; recent preprints (the newest stuff is here).
Journal papers
Frameworks with coordinated edge motions
SIAM Journal on Discrete Mathematics
, 2022.
Transverse rigidity is prestress stability
Discrete Applied Mathematics
, 2022.
Realizations of isostatic material frameworks
physica status solidi (b)
, 2021.
Hidden symmetries generate rigid folding mechanisms in periodic origami
Proc. of the National Academy of Sciences
, 2020.
Almost-rigidity of frameworks
Communications on Pure and Applied Mathematics
, 2020.
Algebraic matroids in action
The American Mathematical Monthly
, 2020.
Generically globally rigid graphs have generic universally rigid frameworks
Combinatorica
, 2020.
Generic unlabeled global rigidity
Forum of Mathematics, Sigma
, 2019.
Rigidity for sticky disks
Proc. of the Royal Society A
, 2019.
Analytic analysis of auxetic metamaterials through analogy with rigid link systems
Proc. of the Royal Society A
, 2018.
Affine rigidity and conics at infinity
International Mathematics Research Notices
, 2017.
Detecting dependencies in geometric constraint systems
Computer Aided Geometric Design
, 2016.
Anchored boundary conditions for locally isostatic networks
Physical Review E
, 2015.
Universality theorems for inscribed polytopes and Delaunay triangulations
Discrete & Computational Geometry
, 2015.
Frameworks with forced symmetry I: reflections and rotations
Discrete & Computational Geometry
, 2015.
The algebraic combinatorial approach for Low-Rank Matrix Completion
Journal of Machine Learning Research
, 2015.
Frameworks with forced symmetry II: orientation-preserving crystallographic groups
Geometriae Dedicata
, 2014.
Generic combinatorial rigidity of periodic frameworks
Advances in Mathematics
, 2013.
Topological designs
Geometriae Dedicata
, 2013.
Natural realizations of sparsity matroids
Ars Mathematica Contemporanea
, 2011.
Slider-pinning rigidity: a Maxwell–Laman-type theorem
Discrete & Computational Geometry
, 2010.
Sparse hypergraphs and pebble game algorithms
European Journal of Combinatorics
, 2009.
Sparsity-certifying graph decompositions
Graphs and Combinatorics
, 2009.
Characterizing sparse graphs by map decompositions
Journal of Combinatorial Mathematics and Combinatorial Computing
, 2007.
Graded sparse graphs and matroids
Journal of Universal Computer Science
, 2007.
Refereed conferences
Delaunay triangulations with disconnected realization spaces
In: Proc. of SoCG
, 2014.
Detecting dependencies in geometric constraint systems
In: Proc. of ADG
, 2014.
Generic rigidity with forced symmetry and sparse colored graphs
In: Proc. of Fields Workshop on Rigidity and Symmetry
, 2014.
Error-Minimizing Estimates and Universal Entry-Wise Error Bounds for Low-Rank Matrix Completion
In: Proc. of NIPS
, 2013.
Rigid components in fixed-lattice and cone frameworks
In: Proc. of CCCG
, 2011.
Searching in tree-like partial orders
In: Proc. of WADS
, 2011.
The rigidity transition in random graphs
In: Proc. of SODA
, 2011.
Rigid components of random graphs
In: Proc. of CCCG
, 2009.
Combinatorial genericitity and minimal rigidity
In: Proc. of SoCG
, 2008.
Analyzing rigidity with pebble games
In: Proc. of SoCG
, 2008.
The slider-pinning problem
In: Proc. of CCCG
, 2007.
Finding and maintaining rigid components
In: Proc. of CCCG
, 2005.
Preprints
General position stresses
Preprint
, 2023.
Universal Rigidity of Ladders on the line
Preprint
, 2022.
Computing maximum likelihood thresholds using graph rigidity
Preprint
, 2022.
Maximum likelihood thresholds via graph rigidity
Preprint
, 2021.
Global rigidity of complete bipartite graphs
Preprint
, 2021.
Universal rigidity on the line, point order
Preprint
, 2021.
Reconstruction in one dimension from unlabeled Euclidean lengths
Preprint
, 2020.
Algebraic-combinatorial methods for low-rank matrix completion with application to athletic performance prediction
Preprint
, 2014.
Learning with Cross-Kernels and Ideal PCA
Preprint
, 2014.
Ultrarigid periodic frameworks
Preprint
, 2014.
Matroid regression
Preprint
, 2014.
Dual-to-kernel learning with ideals
Preprint
, 2014.
Algebraic matroids with graph symmetry
Preprint
, 2013.
Coherence and sufficient sampling densities for reconstruction in compressed sensing
Preprint
, 2013.
Generic rigidity of reflection frameworks
Preprint
, 2012.
Henneberg constructions and covers of cone-Laman graphs
Preprint
, 2012.
Lines induced by bichromatic point sets
Preprint
, 2011.