Xavier Goaoc

Professor of computer science,
Université de Lorraine, Nancy



Welcome to my professional web page. Here you'll find information on my research and my teaching activities.

Picture by Otfried Cheong

Since 2018, I work at at Université de Lorraine in Nancy. I am affiliated with the department of computer science & engineering of École des Mines de Nancy. I am also a member the Gamble research team, joint between the LORIA laboratory and the INRIA research center.

Here is a short cv.

Research

Loria
bureau B166
615 rue du jardin botanique
54600 Villers-les-Nancy


xavier.goaoc@loria.fr
(+33) 3 54 95 85 37

Teaching

École des Mines, Campus Artem
bureau R329
CS 14234
54042 Nancy cedex
xavier.goaoc@univ-lorraine.fr
(+33) 3 72 74 49 62

  • algorithmes et complexité. Cours de tronc commun de 1ère année (9x3h). Introduit à l'informatique théorique (modèles de calcul, conception et analyse d'algorithmes, complexité des problèmes, NP-difficulté).

  • architecture des ordinateurs. Cours de 2ème année du département informatique (7x3h). Aborde les hiérarchies mémoire, l'assembleur x86 et l'analyse de code compilé par gcc, le pipeline et la prédiction de branchement, la vectorisation.

  • introductions aux blockchaines. Cours électif de 2ème année (7x3h). Aborde le hachage et les signatures cryptographique, les principes de calcul distribué, les principes de la blockchaine de bitcoin, le théorème de Fischer, Lynch, Paterson et le théorème Lamport-Shostak-Pease, les algorithmes Paxos et BBA*.
  • En 1A Mines, algorithmes et complexité
  • En 2A Mines, architecture des ordinateurs
  • En 2A Mines, introduction aux blockchains
  • En M2, modélisation géométrique et planification de trajectoire
  • En 5A Polytech, algorithmes de consensus et blockchains
  • 2021-2022 : architecture avancée, introduction aux blockchaines, algorithmes et complexité, consensus et blockchains
  • 2020-2021 : algorithmique avancée, architecture avancée, introduction aux blockchaines, algorithmes et complexité, algorithmique distribuée, apprentissage automatique (TD), recherche opérationnelle (TD)
  • 2019-2020 : algorithmique avancée, architecture avancée, introduction aux blockchaines, recherche opérationelle (TD), algorithmique-programmation (TD)
  • 2018-2019 : algorithmique avancée, architecture avancée
  • 2017-2018 : architecture avancée, mathématiques discrètes (isopérimétries), fondements de l'optimisation
  • 2016-2017 : architecture avancée, mathématiques discrètes (isopérimétries)
  • 2015-2016 : architecture des ordinateurs, mathématiques discrètes (géométrie)
  • 2014-2015 : optimisation combinatoire, architecture des ordinateurs
  • 2013-2014 : architecture des ordinateurs, probabilités pour informaticien, programmation en C, optimisation combinatoire, mathématiques discrètes pour informaticiens

My research is in algorithms and discrete mathematics, more precisely in the area of discrete and computational geometry. I am particularly interested in its interactions with topology, probability and extremal combinatorics.

Here is a complete list of my publications.

Below are my main publications organized by topics. You'll find some of my papers on arXiv and on HAL.

INRIA associate team FIP


(A handful of papers appear in more than one topic.)


Uli Wagner proposed an homological version of graph minors for simplicial complexes. Here are some applications of this notion.
Abstract simplicial complex are elementary combinatorial structures, really a subclass of hypergraphs, that, like planar graphs, can be interpreted as triangulations of topological spaces. Their study combines combinatorics and topology beautifully.
These papers investigate the combinatorial complexity of discrete structures (such as polytopes) defined by random point sets.
Order types are combinatorial structures that arise from finite (planar) point sequences, in the same way as permutations arise from finite sequences of real numbers. I am interested in random generation methods that produce "interesting" order types. This proves surprisingly difficult...
Combinatorial convexity studies the intersection patterns of families of convex sets, with a particular attention to the systems of convex hulls of finite subsets of a point set. It grew out of the theorems of Helly, Radon and Carathéodory and flourished in a rich and beautiful theory with surprising connections. I am interested in relaxing convexity into weaker topological assumptions.
Combinatorial convexity can be extended by considering not only points common to families of convex sets, but lines piercing families of convex sets. See here for a sample. I am interested in geometric permutations and worked on some conjectures of Danzer.
I am also fond of the application of line geometry (as pioneered by Klein, Plücker, ...) to the analysis of geometric models of imaging systems.