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

Reconstruction in one dimension from unlabeled Euclidean lengths
Combinatorica
, 2024.
  • Robert Connelly
  • Steven J. Gortler
  • Louis Theran
Maximum likelihood thresholds via graph rigidity
Annals of Applied Probability
, 2024.
  • Daniel Bernstein
  • Sean Dewar
  • Steven J. Gortler
  • Anthony Nixon
  • Meera Sitharam
  • Louis Theran
Computing maximum likelihood thresholds using graph rigidity
Algebraic Statistics
, 2023.
  • Daniel Bernstein
  • Sean Dewar
  • Steven J. Gortler
  • Anthony Nixon
  • Meera Sitharam
  • Louis Theran
Frameworks with coordinated edge motions
SIAM Journal on Discrete Mathematics
, 2022.
  • Bernd Schulze
  • Hattie Serocold
  • Louis Theran
Transverse rigidity is prestress stability
Discrete Applied Mathematics
, 2022.
  • Steven J. Gortler
  • Miranda Holmes-Cerfon
  • Louis Theran
Realizations of isostatic material frameworks
physica status solidi (b)
, 2021.
  • Mahdi Sadjadi
  • Varda F. Hagh
  • Mingyu Kang
  • Meera Sitharam
  • Robert Connelly
  • Steven J. Gortler
  • Louis Theran
  • Miranda Holmes-Cerfon
  • Michael Thorpe
Hidden symmetries generate rigid folding mechanisms in periodic origami
Proc. of the National Academy of Sciences
, 2020.
  • James McInerney
  • Bryan Gin-ge Chen
  • Louis Theran
  • Chris Santangelo
  • Zeb Rocklin
Almost-rigidity of frameworks
Communications on Pure and Applied Mathematics
, 2020.
  • Miranda Holmes-Cerfon
  • Louis Theran
  • Steven J. Gortler
Algebraic matroids in action
The American Mathematical Monthly
, 2020.
  • Zvi Rosen
  • Jessica Sidman
  • Louis Theran
Generically globally rigid graphs have generic universally rigid frameworks
Combinatorica
, 2020.
  • Robert Connelly
  • Steven J. Gortler
  • Louis Theran
Generic unlabeled global rigidity
Forum of Mathematics, Sigma
, 2019.
  • Steven J. Gortler
  • Louis Theran
  • Dylan P. Thurston
Rigidity for sticky disks
Proc. of the Royal Society A
, 2019.
  • Robert Connelly
  • Steven J. Gortler
  • Louis Theran
Analytic analysis of auxetic metamaterials through analogy with rigid link systems
Proc. of the Royal Society A
, 2018.
  • Daniel Rayneau-Kirkhope
  • Chengzhao Zhang
  • Louis Theran
  • Marcelo A. Dias
Affine rigidity and conics at infinity
International Mathematics Research Notices
, 2017.
  • Robert Connelly
  • Steven J. Gortler
  • Louis Theran
Detecting dependencies in geometric constraint systems
Computer Aided Geometric Design
, 2016.
  • James Farre
  • Helena Kleinschmidt
  • Jessica Sidman
  • Audrey Lee-St. John
  • Stephanie Stark
  • Louis Theran
  • Xilin Yu
Anchored boundary conditions for locally isostatic networks
Physical Review E
, 2015.
  • Louis Theran
  • Anthony Nixon
  • Elissa Ross
  • Mahdi Sadjadi
  • Brigitte Servatius
  • Michael Thorpe
Universality theorems for inscribed polytopes and Delaunay triangulations
Discrete & Computational Geometry
, 2015.
  • Karim A. Adiprasito
  • Arnau Padrol
  • Louis Theran
Frameworks with forced symmetry I: reflections and rotations
Discrete & Computational Geometry
, 2015.
  • Justin Malestein
  • Louis Theran
The algebraic combinatorial approach for Low-Rank Matrix Completion
Journal of Machine Learning Research
, 2015.
  • Franz J. Király
  • Louis Theran
  • Ryota Tomioka
Frameworks with forced symmetry II: orientation-preserving crystallographic groups
Geometriae Dedicata
, 2014.
  • Justin Malestein
  • Louis Theran
Generic combinatorial rigidity of periodic frameworks
Advances in Mathematics
, 2013.
  • Justin Malestein
  • Louis Theran
Topological designs
Geometriae Dedicata
, 2013.
  • Justin Malestein
  • Igor Rivin
  • Louis Theran
Natural realizations of sparsity matroids
Ars Mathematica Contemporanea
, 2011.
  • Ileana Streinu
  • Louis Theran
Slider-pinning rigidity: a Maxwell–Laman-type theorem
Discrete & Computational Geometry
, 2010.
  • Ileana Streinu
  • Louis Theran
Sparse hypergraphs and pebble game algorithms
European Journal of Combinatorics
, 2009.
  • Ileana Streinu
  • Louis Theran
Sparsity-certifying graph decompositions
Graphs and Combinatorics
, 2009.
  • Ileana Streinu
  • Louis Theran
Characterizing sparse graphs by map decompositions
Journal of Combinatorial Mathematics and Combinatorial Computing
, 2007.
  • Ruth Haas
  • Audrey Lee
  • Ileana Streinu
  • Louis Theran
Graded sparse graphs and matroids
Journal of Universal Computer Science
, 2007.
  • Audrey Lee
  • Ileana Streinu
  • Louis Theran

Refereed conferences

Delaunay triangulations with disconnected realization spaces
In: Proc. of SoCG
, 2014.
  • Arnau Padrol
  • Louis Theran
Detecting dependencies in geometric constraint systems
In: Proc. of ADG
, 2014.
  • James Farre
  • Helena Kleinschmidt
  • Jessica Sidman
  • Audrey Lee-St. John
  • Stephanie Stark
  • Louis Theran
Generic rigidity with forced symmetry and sparse colored graphs
In: Proc. of Fields Workshop on Rigidity and Symmetry
, 2014.
  • Justin Malestein
  • Louis Theran
Rigid components in fixed-lattice and cone frameworks
In: Proc. of CCCG
, 2011.
  • Matthew Berardi
  • Brent Heeringa
  • Justin Malestein
  • Louis Theran
Searching in tree-like partial orders
In: Proc. of WADS
, 2011.
  • Brent Heeringa
  • Marius Cătălin Iordan
  • Louis Theran
The rigidity transition in random graphs
In: Proc. of SODA
, 2011.
  • Shiva Kasiviswanathan
  • Cristopher Moore
  • Louis Theran
Rigid components of random graphs
In: Proc. of CCCG
, 2009.
  • Louis Theran
Combinatorial genericitity and minimal rigidity
In: Proc. of SoCG
, 2008.
  • Ileana Streinu
  • Louis Theran
Analyzing rigidity with pebble games
In: Proc. of SoCG
, 2008.
  • Audrey Lee
  • Ileana Streinu
  • Louis Theran
The slider-pinning problem
In: Proc. of CCCG
, 2007.
  • Audrey Lee
  • Ileana Streinu
  • Louis Theran
Finding and maintaining rigid components
In: Proc. of CCCG
, 2005.
  • Audrey Lee
  • Ileana Streinu
  • Louis Theran

Preprints

General position stresses
Preprint
, 2023.
  • Robert Connelly
  • Steven J. Gortler
  • Louis Theran
Maximum likelihood thresholds of generic linear concentration models
Preprint
, 2023.
  • Daniel Bernstein
  • Steven J. Gortler
  • Louis Theran
Universal Rigidity of Ladders on the line
Preprint
, 2022.
  • Bryan Gin-ge Chen
  • Robert Connelly
  • Steven J. Gortler
  • Anthony Nixon
  • Louis Theran
Global rigidity of complete bipartite graphs
Preprint
, 2021.
  • Robert Connelly
  • Steven J. Gortler
  • Louis Theran
Universal rigidity on the line, point order
Preprint
, 2021.
  • Robert Connelly
  • Steven J. Gortler
  • Louis Theran
Determining generic point configurations from unlabeled path or loop lengths
Preprint
, 2017.
  • Ioannis Gkioulekas
  • Steven J. Gortler
  • Louis Theran
  • Todd Zickler
Learning with Cross-Kernels and Ideal PCA
Preprint
, 2014.
  • Franz J. Király
  • Martin Kreuzer
  • Louis Theran
Ultrarigid periodic frameworks
Preprint
, 2014.
  • Justin Malestein
  • Louis Theran
Matroid regression
Preprint
, 2014.
  • Franz J. Király
  • Louis Theran
Dual-to-kernel learning with ideals
Preprint
, 2014.
  • Franz J. Király
  • Martin Kreuzer
  • Louis Theran
Algebraic matroids with graph symmetry
Preprint
, 2013.
  • Franz J. Király
  • Zvi Rosen
  • Louis Theran
Generic rigidity of reflection frameworks
Preprint
, 2012.
  • Justin Malestein
  • Louis Theran
Lines induced by bichromatic point sets
Preprint
, 2011.
  • Louis Theran