Here is a list of publication by chronological order and another one by publication type (on HAL).
1. Combinatorial geometry and topology
A survey of relations between five elementary results in
discrete topology and discrete geometry, as well as applications in
game theory and fair division, graph theory, optimization and
geometric data analysis.

The discrete yet ubiquitous theorems of CarathÃ©odory, Helly, Sperner, Tucker, and Tverberg
J. A. De Loera, X. Goaoc, F. Meunier and N. Mustafa
Some complexity results...

Shellability is NPcomplete
X. Goaoc, P. Paták, Z. Patáková, M. Tancer, and U. Wagner

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

Simplifying inclusionexclusion formulas
X. Goaoc, J. Matousek, P. Paták, Z. Safernová, and M. Tancer
Some results around nonembeddability...

Bounding Helly numbers via Betti numbers
X. Goaoc, P. Paták, Z. Safernová, M. Tancer, and U. Wagner

On generalized Heawood inequalities for manifolds: a Van KampenFlorestype nonembeddability result
X. Goaoc, I. Mabillard, P. Paták, Z. Patáková, M. Tancer, and U. Wagner
A study of intersection pattern via generalized
nerve complexes, with application to geometric
transversal theory.

Multinerves and Helly numbers of acyclic families
E. Colin De Verdière, G. Ginot, and X. Goaoc
Proceedings of
SoCG 2012 (under a slightly different name)
2. Random geometric structures
These papers examine some geometric structures (convex hull and Delaunay triangulation) induced by random point sets.

Smoothed complexity of convex hulls by witnesses and collectors
O. Devillers, M. Glisse, X. Goaoc, and R. Thomasse.
Expands two earlier conference papers:

On the smoothed complexity of convex hulls
O. Devillers, M. Glisse, X. Goaoc, and R. Thomasse.

Complexity analysis of random geometric structures made simpler
O. Devillers, M. Glisse, and X. Goaoc.
see also the Inria research reports
8168 and
7134

The monotonicity of fvectors of random polytopes
O. Devillers, M. Glisse, X. Goaoc, G. Moroz, and M. Reitzner

Emptyellipse graphs
O. Devillers, J. Erickson, and X. Goaoc
Proceedings of SODA 2008 (pp. 12491257)
pdf file (No journal version is planned)
3. Extremal combinatorics for geometry
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
Some papers exploring questions on line geometry raised by computer vision.

Consistent sets of lines with no colorful incidence
B. Bukh, X. Goaoc, A. Hubard, and M. Tragger
Accepted to SoCG 2018

Admissible Linear Map Models of Linear Cameras
G. Batog, X. Goaoc, and J. Ponce
In how many different ways, that is geometric permutations, can one stab disjoint unit balls?

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
A proof of a Hellytype theorem for sets of line
transversals to disjoint unit balls conjectured by
Danzer and related questions.

HellyType Theorems for Line Transversals to Disjoint Unit Balls
O. Cheong, X. Goaoc, A. Holmsen, and S. Petitjean

Line transversals to disjoint balls
C. Borcea, X. Goaoc, and S. Petitjean

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
Hellytype theorems for isolated line transversals.

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
Overview of how the three topics above (geometric permutations, Danzer's conjecture and Hellytype theorems for isolated transversals) are related.

Transversal Helly numbers, pinning theorems and projection of simplicial complexes
Habilitation thesis from Université Henri Poincaré  Nancy 1, December 2011

Some Discrete Properties of the Space of Line Transversals to Disjoint Balls
X. Goaoc
5. 3D visibility
Approximate algorithms for visibility query from Hellytype theorems.

Hellytype theorems for approximate covering
J. Demouth, O. Devillers, M. Glisse, and X. Goaoc
Some bounds on the complexity of data structures for 3D visibility.

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
A characterization of degeneracies for visibiility among balls in 3D.

Common Tangents to Spheres in R^{3}
C. Borcea, X. Goaoc, S. Lazard, and S. Petitjean
My PhD thesis, gathering (and expanding) the two topics above: complexity an degeneracies of 3D visibility structures.

Structures de visibilité globale : taille, calcul et dégénerescences
PhD thesis from Université Nancy 2, May 2004
6. Other topics
A reduction of the computation of the shortest bounded curvature path through a sequence of points (in a given order; this is not TSP) 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
Some other various works

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)