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2023
Finding weakly simple closed quasigeodesics on polyhedral spheres.
Jean Chartier and Arnaud de Mesmay.
Discrete and Computational Geometry, 2023.
doi
Measuring pants.
Nhat Minh Doan, Hugo Parlier, and Ser Peow Tan.
Transactions of the American Mathematical Society.
(AMS Early View article, 2023)
doi
Systolic inequalities for the number of vertices.
Sergey Avvakumov, Alexey Balitskiy, Alfredo Hubard, and Roman Karasev.
Journal of Topology and Analysis.
(Online Ready, 2023)
doi
Systoles and diameters of hyperbolic surfaces.
Florent Balacheff, Vincent Despré, and Hugo Parlier.
Kyoto Journal of Mathematics. 63(1): 211--222
(2023)
doi
2022
Enumerating Isotopy Classes of Tilings guided by the symmetry of Triply-Periodic Minimal Surfaces.
Benedikt Kolbe and Myfanwy E Evans.
SIAM Journal on Applied Algebra and Geometry, 2022, 6 (1),
doi
Equipartitions and Mahler volume of symmetric convex bodies.
Mathieu Fradelizzi, Alfredo Hubard, Mathieu Meyer, Edgardo Roldán-Pensado, and Artem Zvavitch.
American Journal of Mathematics, 144(5), 1201--1219
(2022)
doi
Holonomic approximation through convex integration.
Patrick Massot and Mélanie Theillière.
International Mathematics Research Notices
(2022)
doi
Short closed geodesics on cusped hyperbolic surfaces.
Hanh Vo.
Pacific Journal of Mathematics, 318(1), 127–-151
(2022)
doi
Embedding graphs into two-dimensional simplicial complexes.
Éric Colin de Verdière, Thomas Magnard, and Bojan Mohar.
Computing in Geometry and Topology, 1(1):6
(2022)
Minimal Delaunay triangulations of hyperbolic surfaces.
Matthijs Ebbens, Hugo Parlier, and Gert Vegter.
Discrete & Computational Geometry
(2022)
doi
Weakly Inscribed Polyhedra.
Hao Chen and Jean-Marc Schlenker.
Transactions of the American Mathematical Society, Series B. 9, 415--449
(2022)
doi
Tightening Curves on Surfaces Monotonically with Applications.
Hsien-Chih Chang and Arnaud de Mesmay.
ACM Transactions on Algorithms. 18(4), 1-–32
(2022)
doi
Algorithms for Contractibility of Compressed Curves on 3-Manifold Boundaries.
Erin Wolf Chambers, Francis Lazarus, Arnaud de Mesmay, and Salman Parsa.
Discrete & Computational Geometry
(2022)
doi
Delaunay triangulations of generalized Bolza surfaces.
Matthijs Ebbens, Iordan Iordanov, Monique Teillaud, and Gert Vegter.
Journal of Computational Geometry. 13(1), 125--177
(2022)
Tile-transitive tilings of the Euclidean and hyperbolic planes by ribbons.
Benedikt Kolbe and Vanessa Robins.
Research in Computational Topology 2. Association for Women in Mathematics Series, vol 30. 77--98
(2022)
doi
2021
Polytopal balls arising in optimization.
Antoine Deza, Jean-Baptiste Hiriart-Urruty, and Lionel Pournin.
Contributions to Discrete Mathematics 15(3), 125–-138
(2021)
doi
The minimal length product over homology bases of manifolds.
Florent Balacheff, Steve Karam, and Hugo Parlier.
Mathematische Annalen, 380, 825–-854
(2021)
doi
A Near-Linear Approximation Scheme for Multicuts of Embedded Graphs with a Fixed Number of Terminals.
Vincent Cohen-Addad, Éric Colin de Verdière, and Arnaud de Mesmay.
SIAM Journal of Computing, 50(1), 1-–31
(2021)
doi
Almost Tight Lower Bounds for Hard Cutting Problems in Embedded Graphs.
Vincent Cohen-Addad, Éric Colin de Verdière, Dániel Marx, and Arnaud de Mesmay.
Journal of the ACM, 68(4), 30:1--30:26
(2021)
doi
The vertices of primitive zonotopes.
Antoine Deza, Lionel Pournin, and Rado Rakotonarivo.
AMS Special Session Polytopes and Discrete Geometry. Contemporary Mathematics, 764, 71--82
(2021)
doi
Quadratic differentials and circle patterns on complex projective tori.
Wai Yeung Lam.
Geometry & Topology, 25(2), 961--997
(2021)
doi
2020
Embeddability of arrangements of pseudocircles on surfaces.
Éric Colin de Verdière, Carolina Medina, Edgardo Roldán-Pensado, and Gelasio Salazar.
Discrete & Computational Geometry, 64, 386--395
(2020)
doi
The diameter of lattice zonotopes.
Antoine Deza, Lionel Pournin, and Noriyoshi Sukegawa.
Proceedings of the American Mathematical Society 148(8), 3507--3516
(2020)
doi
Elementary moves on lattice polytopes.
Julien David, Lionel Pournin, and Rado Rakotonarivo.
Journal of Combinatorial Theory A 172, 105200
(2020)
doi
Distance between vertices of lattice polytopes.
Anna Deza, Antoine Deza, Zhongyan Guan, and Lionel Pournin.
Optimization Letters 14, 309--326
(2020)
doi
Geometric simplicial embeddings of arc-type graphs.
Hugo Parlier and Ashley Weber.
Journal of the Korean Mathematical Society 57(5), 1103--1118
(2020)
doi
2019
Diameter, decomposability, and Minkowski sums of polytopes.
Antoine Deza and Lionel Pournin.
Canadian Mathematical Bulletin 62(4), 741--755
(2019)
doi
Eccentricities in the flip-graphs of convex polygons.
Lionel Pournin.
Journal of Graph Theory 92(2), 111--129
(2019)
doi
2023
Disjoint faces in simple drawings of the complete graph and topological Heilbronn problems.
Alfredo Hubard and Andrew Suk.
Proceedings 39th International Symposium on Computational Geometry.
To appear (2023)
Invited at Discrete and Computational Geometry (SoCG'23 special issue)
Computing a Dirichlet domain for a hyperbolic surface.
Vincent Despré, Benedikt Kolbe, Hugo Parlier, and Monique Teillaud.
Proceedings 39th International Symposium on Computational Geometry.
To appear (2023)
Invited at Journal of Computational Geometry (SoCG'23 special issue)
A structural approach to tree decompositions of knots and spatial graphs.
Corentin Lunel and Arnaud de Mesmay.
Proceedings 39th International Symposium on Computational Geometry.
To appear (2023)
2022
A bound for Delaunay flip algorithms on flat tori.
(full proceedings)
Loïc Dubois.
34th Canadian Conference on Computational Geometry, 105--112
(2022)
(Best Student Paper Award)
Finding Weakly Simple Closed Quasigeodesics on Polyhedral Spheres.
Jean Chartier and Arnaud de Mesmay.
Proceedings 38th International Symposium on Computational Geometry, 27:1--27:16
(2022)
Short Topological Decompositions of Non-Orientable Surfaces.
Niloufar Fuladi, Alfredo Hubard, and Arnaud de Mesmay.
Proceedings 38th International Symposium on Computational Geometry, 41:1--41:16
(2022)
2021
Algorithms for Contractibility of Compressed Curves on 3-Manifold Boundaries.
Erin Wolf Chambers, Francis Lazarus, Arnaud de Mesmay, and Salman Parsa.
Proceedings 37th International Symposium on Computational Geometry, 23:1--23:16
(2021)
Minimal Delaunay triangulations of hyperbolic surfaces.
Matthijs Ebbens, Hugo Parlier, and Gert Vegter.
Proceedings 37th International Symposium on Computational Geometry, 31:1--31:16
(2021)
An FPT Algorithm for the Embeddability of Graphs into Two-Dimensional Simplicial Complexes.
Éric Colin de Verdière and Thomas Magnard.
Proceedings 29th European Symposium on Algorithms, 32:1--32:17
(2021)
2020
Tightening Curves on Surfaces Monotonically with Applications.
Hsien-Chih Chang and Arnaud de Mesmay.
Proceedings of the ACM-SIAM Symposium on Discrete Algorithms
(2020)
doi
Flipping Geometric Triangulations on Hyperbolic Surfaces.
Vincent Despré, Jean-Marc Schlenker, and Monique Teillaud.
Proceedings 36th International Symposium on Computational Geometry, 35:1--35:16
(2020)
Generalizing CGAL Periodic Delaunay Triangulations.
Georg Osang, Mael Rouxel-Labbé, and Monique Teillaud.
Proceedings 28th European Symposium on Algorithms, 75:1--75:17
(2020)
(Best Paper Award - Track B: Engineering and Applications).
2019
Almost Tight Lower Bounds for Hard Cutting Problems in Embedded Graphs.
Vincent Cohen-Addad, Éric Colin de Verdière, Daniel Marx, and Arnaud de Mesmay.
Proceedings 35th International Symposium on Computational Geometry, 27:1--27:16
(2019)
(Best Paper Award).
2018
Embedding graphs into two-dimensional simplicial complexes.
Éric Colin de Verdière, Thomas Magnard, and Bojan Mohar.
Proceedings 34th International Symposium on Computational Geometry, 27:1--27:14,
(2018)
2020
Triangulations in CGAL: to non-Euclidean spaces... and Beyond!
Monique Teillaud.
36th European Workshop on Computational Geometry
(2020)
2021
2D Triangulations on the Sphere.
Mael Rouxel-Labbé, Monique Teillaud, and Claudia Werner.
CGAL User and Reference Manual, 5.3 edition.
The CGAL Editorial Board, editor.
(2021).
source code on github
2019
2D Hyperbolic Delaunay Triangulations.
Mikhail Bogdanov, Iordan Iordanov, and Monique Teillaud.
CGAL User and Reference Manual, 4.14 edition.
The CGAL Editorial Board, editor.
(2019).
source code on github
2D Periodic Hyperbolic Triangulations.
Iordan Iordanov and Monique Teillaud.
CGAL User and Reference Manual, 4.14 edition.
The CGAL Editorial Board, editor.
(2019).
source code on github
2023
A linear bound for the Colin de Verdière parameter µ for graphs embedded on surfaces.
Camille Lanuel, Francis Lazarus, and Rudi Pendavingh.
39th European Workshop on Computational Geometry
(2023)
2022
Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces.
Vincent Despré, Loïc Dubois, Benedikt Kolbe, and Monique Teillaud.
38th European Workshop on Computational Geometry
(2022)
2020
Enumerating tilings of triply-periodic minimal surfaces with rotational symmetries.
Benedikt Kolbe and Myfanwy Evans.
36th European Workshop on Computational Geometry
(2020)
2019
Delaunay triangulations of symmetric hyperbolic surfaces.
Matthijs Ebbens, Iordan Iordanov, Monique Teillaud, and Gert Vegter.
35th European Workshop on Computational Geometry
(2019)
2018
Delaunay triangulations of regular hyperbolic surfaces (abstract).
Matthijs Ebbens, Iordan Iordanov, Monique Teillaud, and Gert Vegter.
9th International Conference on Curves and Surfaces
(2018)
Systole of regular hyperbolic surfaces with an application to Delaunay triangulations (abstract).
Matthijs Ebbens, Iordan Iordanov, Monique Teillaud, and Gert Vegter.
9th International Conference on Curves and Surfaces
(2018)
2023
A Structural Approach to Tree Decompositions of Knots and Spatial Graphs.
Corentin Lunel and Arnaud de Mesmay.
Universal families of arcs and curves on surfaces.
Niloufar Fuladi, Arnaud de Mesmay, and Hugo Parlier.
A linear bound for the Colin de Verdière parameter µ for graphs embedded on surfaces.
Camille Lanuel, Francis Lazarus, and Rudi Pendavingh.
2022
The coarse geometry of hexagon decomposition graphs.
Funda Gültepe and Hugo Parlier.
2021
Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces.
Vincent Despré, Loïc Dubois, Benedikt Kolbe, and Monique Teillaud.
Strong convexity in flip-graphs.
Lionel Pournin and Zili Wang.
2020
Deciding when two curves are of the same type.
Juan Souto and Thi Hanh Vo.
Towards a combinatorial algorithm for the enumeration of isotopy classes of tilings on hyperbolic surfaces.
Benedikt Kolbe.
Half-minimizers and Delaunay triangulations on closed hyperbolic surfaces.
Vincent Despré, Benedikt Kolbe, and Monique Teillaud.
CMC-1 surfaces via osculating Möbius transformations between circle patterns.
Wai Yeung Lam.
2018
Quantifying the sparseness of simple geodesics on hyperbolic surfaces.
Peter Buser and Hugo Parlier.
Delaunay Triangulations of Points on Circles.
Vincent Despré, Olivier Devillers, Hugo Parlier, and Jean-Marc Schlenker.