Curriculum vitae: Louis Theran
School of Mathematics and Statistics
University of St Andrews
Fife KY16 9SS
Research interests
My research focus is the rigidity theory of frameworks.
More broadly, I'm interested in discrete geometry, combinatorics, machine learning,
algorithms, and the interactions between these areas. I work on
theoetical and applied problems.
Education
9.2010:
Ph.D.,
Computer Science,
University of Massachusetts, Amherst.
Dissertation: Problems in generic combinatorial rigidity: sparsity, sliders, and emergence of components
Advisor: Ileana Streinu
9.2007:
M.S.,
Computer Science,
University of Massachusetts, Amherst.
2.2006:
B.S.,
Computer Science and Mathematics,
University of Massachusetts, Amherst.
Honors: cum laude
Academic positions
Affiliated member of Department of Information and Computer Science
Cofunded by AKA project COALESCE (PI: Petteri Kaski)
Supported by the ERC Advance Grant Project SD-Models (PI: Günter M. Ziegler)
Post-doctoral appointment
Supported by NSF CDI-I grant DMR 0835586 (PIs: Igor Rivin and M. M. J. Treacy)
Graduate student appointment
Supervised by Ileana Streinu
Industry positions
2000–2001:
Senior Software Engineer,
Nokia Research Center (Boston)
1999–2000:
Software Engineer,
Nokia Research Center (Boston)
1998–1999:
Software Engineer,
Nokia Wireless Software Solutions (Boston)
1996–1998:
Software Engineer,
Open Software Foundation Research Institute (Cambridge)
Funding
2021:
Heilbronn small grants scheme
Discrete structures: algebra, combinatorics and geometry
PI (co-PIs Daniel Bernstein and Tony Nixon). £3,100
2014–2017:
AScI Thematic Program
Challenges in Large Geometric Structures and Big Data
PI and coordinator
2006:
NSF/KOSEF East Asia and Pacific Summer Institutes Fellowship
(NSF OISE-0611980)
Supported a Summer visit to KAIST
Publications
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.
Teaching
Courses
S2 2017-2018, S2 2019-2020:
Discrete Geometry (MT5862)
(15 cr)
University of St Andrews
S2 2017-2018, S2 2019-2020:
Topology (MT4526)
(15 cr)
University of St Andrews
S2 2016–2017, S2 2018–2019:
Symbolic Computation (MT4111/5611)
(15 cr)
University of St Andrews
S1 2017–2018:
Linear mathematics 2 (MT3501)
(15 cr)
University of St Andrews
S1 2017–2018, S2 2020–2021:
Combinatorics and probability (MT2504)
(15 cr)
University of St Andrews
S1 2020–2021:
Mathematics (MT1002)
(20 cr)
University of St Andrews
S1 2016–2017:
Introductory Mathematics (MT1001)
(20 cr)
University of St Andrews
Fall 2014:
Computational geometry
(5 cr)
Aalto University, master's course
Spring 2012:
Rigidity theory
(4 hr)
Freie Universität Berlin, Discrete Geometry III module
Spring 2010:
Graph theory
(4 cr)
Temple University, master's course
Fall 2010:
Algorithms
(4 cr)
Temple University, PhD core course
Spring 2009:
Discrete and computational geometry
(4 cr)
Temple University, undergraduate capstone course
Fall 2009:
Combinatorics
(4 cr)
Temple University, undergratuate elective
Seminars
Summer 2014:
Tilings
(2 hr)
Freie Universität Berlin, undergraduate ProSeminar
Winter 2014:
Triangle tiling
(2 hr)
Freie Universität Berlin, undergraduate ProSeminar
Summer 2013:
Sphere packing
(2 hr)
Freie Universität Berlin, undergraduate ProSeminar
Service
Dissertation committees
2021:
Luke Elliot,
University of St Andrews,
School of Mathematics and Statistics
Thesis title:
2020:
Nayab Kahlid,
University of St Andrews,
School of Mathematics and Statistics
Thesis title:
2019:
Sean Dewar,
Lancaster University,
Department of Mathematics and Statistics
Thesis title:
2018:
Katie Clinch,
Queen Mary University of London,
School of Mathematical Sciences
Thesis title:
2017:
Tom Bourne,
University of St Andrews,
School of Mathematics and Statistics
Thesis title:
2013:
Anita Liebenau,
Freie Universität Berlin,
Berlin Mathematical School
Thesis title: Orientation Games and Minimal Ramsey Graphs
2011:
Michael Dobbins,
Temple University,
Department of Mathematics
Thesis title: Representations of polytopes
Bachelor theses and projects
2021:
George O'Rourke,
University of St Andrews,
Thesis title: Turing-tape games
My role: BSc project co-supervisor (maths/cs joint)
2021:
Marley Chinn,
University of St Andrews,
Thesis title: Surreal numbers & combinatorial games
My role: BSc project co-supervisor (maths/cs joint)
2021:
George Tillisch,
University of St Andrews,
Thesis title: Formalising coding theory in Lean
My role: BSc project supervisor
2021:
Mohammad al Attar,
University of St Andrews,
Thesis title: Geometry of manifolds
My role: BSc project supervisor
2020:
Giacomo Fenzi,
University of St Andrews,
Thesis title: Zero knowledge proofs — theory and applications
My role: BSc project co-supervisor (maths/cs)
2020:
Ryan Jarvis,
University of St Andrews,
Thesis title: An introduction to tensegrities
My role: BSc project supervisor
2020:
Ian MacKenzie,
University of St Andrews,
Thesis title: Nearly isostatic networks and allosteric effects
My role: MMath project supervisor
2019:
Christopher White,
University of St Andrews,
Thesis title: The natural correspondence between Steinitz Representations and Colin de Verdière matrices
My role: BSc project supervisor
2019:
Antoine Goldsborough,
University of St Andrews,
Thesis title: Cycle rooted spanning forests and the vector bundle Laplacian
My role: MMath project supervisor
2018:
Jakab Perczel,
University of St Andrews,
Thesis title: Introduction to rigidity theory
My role: BSc project supervisor
2018:
Oliver Vierkins,
University of St Andrews,
Thesis title: Introduction to rigidity theory
My role: BSc project supervisor
2017:
Kestutis Vilcinskas,
University of St Andrews,
Thesis title: Random graphs and graphons
My role: MMath project supervisor
2015:
Lauri Tervonen,
Aalto University,
Computer Science
Thesis title: Strategies in the game Cordial Minuet
My role: Advisor
2014:
Katherina Mölter,
Freie Universität Berlin,
Mathematics
Thesis title: Alternating-sign matrices, square ice, and the Yang-Baxter equation
My role: 2nd examiner
2014:
Jennifer Friedrichs,
Freie Universität Berlin,
Mathematics
Thesis title: Über volumenstarre Fachwerke
My role: 2nd examiner
2011:
Matthew Berardi,
Temple University,
Mathematics
Project topic: Symmetric Laman graphs
My role: supervisor
2011:
Olivia Coplan,
Bryn Mawr College,
Mathematics
Project topic: Connectivity of hypothetical zeolite structures
My role: supervisor
2011:
Garrett Wright,
Temple University,
Mathematics
Project topic: GPGPU linear algebra with Python
My role: supervisor
Conference organization
2.2021:
Workshop on Progress and Open Problems in Rigidity at the Fields Institute
Co-organizer
8.2017:
Mini-symposium on Algebraic Methods in Rigidity Theory at SIAM AG2017
Co-organizer
6.2016:
Summer School on Algebra, Statistics and Combinatorics (Aalto University, Helsinki)
Co-organizer and mini-course lecturer
1.2013:
Special session on Discrete and Computational Geometry at the AMS Joint Math Meetings
Co-organizer
2007:
Fall Workshop on Computational Geometry (FWCG'07)
Local organization (web site)
2006:
Fall Workshop on Computational Geometry (FWCG'06)
Local organization
Departmental service
2021–:
Director of Admissions,
School of Mathematics and Statistics,
University of St Andrews
2020–2021:
co-Director of admissions,
School of Mathematics and Statistics,
University of St Andrews
2018–2020:
Admissions officer,
School of Mathematics and Statistics,
University of St Andrews
2018–:
Pure colloquium organizer,
School of Mathematics and Statistics,
University of St Andrews
2016–2017:
Research Committee,
School of Mathematics and Statistics,
University of St Andrews
2007–2008:
Graduate student representative,
Department of Computer Science,
University of Massachusetts, Amherst
2006:
Department steward, Graduate Employee Organization (student assistant's union),
Department of Computer Science,
University of Massachusetts, Amherst