1. Combinatorial geometry and topology
These papers revisit some classical topics in combinatorial geometry (Helly's theorems, planarity, union complexity...) by topological methods (nerve theorems and homological algebra).
 The discrete yet ubiquitous theorems of CarathÃ©odory, Helly, Sperner, Tucker, and Tverberg
J. A. De Loera, X. Goaoc, F. Meunier and N. Mustafa
 The number of holes in the union of translates of a convex set in three dimensions
B. Aronov, O. Cheong, M. G. Dobbins, and X. Goaoc

On generalized Heawood inequalities for manifolds:
a Van KampenFlorestype nonembeddability result
X. Goaoc, I. Mabillard, P. Paták, Z. Patáková, M. Tancer, and U. Wagner
 Bounding Helly numbers via Betti numbers
X. Goaoc, P. Paták, Z. Safernová, M. Tancer, and U. Wagner
 Simplifying inclusionexclusion formulas
X. Goaoc,
J. Matousek, P. Paták, Z. Safernová, and M. Tancer
 Multinerves and Helly numbers of acyclic families
E. Colin De Verdière, G. Ginot, and X. Goaoc
2. Random geometric structures
These papers examine some geometric structures (convex hull and Delaunay triangulation) induced by random point sets.
3. Extremal combinatorics for geometric structures
These papers adapt to geometric structures some techniques from extremal combinatorics.
 Shatter functions with polynomial growth rates
B. Bukh and X. Goaoc
 Limits of order types
X. Goaoc, A. Hubard, R. de Joannis de Verclos, J.S. Sereni, and Jan Volec
 Set Systems and Families of Permutations with Small Traces,
O. Cheong, X. Goaoc, and C. Nicaud
4. Line geometry and geometric transversals
Linear cameras. This paper presents a fairly general model of imaging systems based on linear line congruences. Explicit formulas for direct and inverse projections as well as stereoreconstruction methods for these models are presented.
 Admissible Linear Map Models of Linear Cameras
G. Batog, X. Goaoc, and J. Ponce
Hellytype theorems for line transversals. In these papers we establish that the Helly number of sets of lines transversals to disjoint balls in R^{d} is between 2d1 and 4d1 (later improved to 4d2 by topological methods, see above). This settled a conjecture of Danzer from 1957. The proof uses bounds on numbers of geometric permutations and a convexity property of sets of directions of line transversals further studied in separate papers.
 Transversal Helly numbers, pinning theorems and projection of simplicial complexes
Habilitation thesis from Université Henri Poincaré  Nancy 1, December 2011
 Lower Bounds to Helly Numbers of Line Transversals to Disjoint Congruent Balls
O. Cheong, X. Goaoc, and A. Holmsen
 Inflating balls is NPhard
G. Batog and X. Goaoc
 Some Discrete Properties of the Space of Line Transversals to Disjoint Balls
X. Goaoc
 Line transversals to disjoint balls
C. Borcea, X. Goaoc, and S. Petitjean
 HellyType Theorems for Line Transversals to Disjoint Unit Balls
O. Cheong, X. Goaoc, A. Holmsen, and S. Petitjean
Geometric permutations. In these papers, we establish bounds on the number of different orders in which a line can intersect a given family of disjoint unit balls in R^{d}. This is one key ingredient of the proof of Danzer's conjecture (see above).
 Geometric permutations of nonoverlapping balls revisited
J.S. Ha, O. Cheong and X. Goaoc
 Geometric permutations of disjoint unit spheres
O. Cheong, X. Goaoc and H.S. Na
Isolated line transversals. Another ingredient of the proof of Danzer's conjecture (see above) is a "local Hellytype theorem" for isolated line transversals to disjoint balls. The following papers study similar properties for polytopes and smooth convex sets.
 Lines Pinning Lines
B. Aronov, O. Cheong, X. Goaoc and G. Rote
 Pinning a Line by Balls or Ovaloids in R^{3}
X. Goaoc, S. Konig, and S. Petitjean
5. 3D visibility
These papers present various results related to the complexity of 3D visibility data structures as well the question of detecting some of their degeneracies.
 Hellytype theorems for approximate covering
J. Demouth, O. Devillers, M. Glisse, and X. Goaoc
 Structures de visibilité globale : taille, calcul et dégénerescences
PhD thesis from Université Nancy 2, May 2004
pdf file
 Common Tangents to Spheres in R^{3}
C. Borcea, X. Goaoc, S. Lazard, and S. Petitjean
 Lines and Free Line Segments Tangent to Arbitrary ThreeDimensional Convex Polyhedra
H. Brönnimann, O. Devillers, V. Dujmovic, H. Everett, M. Glisse, X. Goaoc, S. Lazard, H.S. Na, and S. Whitesides
 The expected number of 3D visibility events is linear
O. Devillers, V. Dujmovic, H. Everett, X. Goaoc, S. Lazard, H.S. Na, and S. Petitjean
6. Other topics
Bounded curvature path planning. In this paper we show that the problem of computing the shortest path through a sequence of points (in a given order; this is not TSP) reduces to a family of convex optimization problems.
 BoundedCurvature Shortest Path Through a Sequence of Points Using Convex Optimization
X. Goaoc, H.S. Kim, and S. Lazard
Misc. Some works more remotely related to my (current or past) centers of interest.
 A note on maximally repeated subpatterns of a point set
V. Cortier, X. Goaoc, M. Lee, and H.S. Na
 Untangling a Planar Graph
X. Goaoc, J. Kratochvil, Y. Okamoto, C.S. Shin, A. Spillner, and A. Wolff
 A polynomialtime algorithm to design push plans for sensorless parts sorting
M. de Berg, X. Goaoc and A. F. Van der Stappen
Proceedings of Robotics Science and Systems (RSS), 2005
pdf file
No journal version is planned