French National Research Agency (ANR) project
GEOLMI - Geometry and Algebra of Linear Matrix Inequalities with Systems Control Applications

Research topics

  • Geometry of determinantal varieties
  • Positive polynomials
  • Computational algebraic geometry
  • Semidefinite programming
  • Systems control applications

    Research areas

  • Pure mathematics (real and complex algebraic geometry)
  • Applied mathematics (computational algebraic geometry, optimization, mathematical programming)
  • Engineering sciences (systems control)


    2011 - 2015


  • Grenoble: Roland Hildebrand, Jérôme Malick, LJK-CNRS, Univ. Joseph Fourier de Grenoble
  • Nice: Laurent Busé, Bernard Mourrain, Evelyne Hubert, INRIA Sophia Antipolis Méditerranée
  • Paris: Jean-Charles Faugère, Mohab Safey El Din, Philippe Trébuchet, Elias Tsigaridas, LIP6-CNRS Univ. Pierre et Marie Curie, INRIA Paris Rocquencourt
  • Pau: Daniele Faenzi, Jean Vallès, LMA-CNRS, Univ. de Pau et des Pays de l'Adour
  • Rennes: Michel Coste, Ronan Quarez, Marie-Françoise Roy, IRMAR-CNRS, Univ. de Rennes
  • Toulouse: Didier Henrion, Jean-Bernard Lasserre, LAAS-CNRS, Univ. de Toulouse


  • Marta Abril Bucero, PhD student supervised by Bernard Mourrain (Nice) from October 2011 to December 2014.
  • Simone Naldi, PhD student co-supervised by Didier Henrion (Toulouse) and Mohab Safey El Din (Paris) from October 2012 to October 2015.
  • Joan Pons Llopis, Post-doctoral associate with Daniele Faenzi and Jean Vallès (Pau), from January to December 2014.


    The project is an outgrowth of a previous PEPS (mutildisciplinary exploratory project) funded by CNRS from January 2008 to December 2009 and which culminated with an international workshop.


  • Spring 2011: the Toulouse group is awarded a grant from the Foundation Simone and Cino Del Duca of the Institut de France, upon recommendation by a committee of the French Academy of Sciences, see this article (in French).

  • 24-25 November 2011: 1st GeoLMI meeting: a workshop is organised by Ronan Quarez (Rennes) in Rennes.

  • 20-24 February 2012: a workshop on Emerging Developments in Real Algebraic Geometry: Positivity, Convexity, NC-Geometry, Optimization is organised by Gennadiy Averkov, Martin Henk (Magdeburg); Salma Kuhlmann, Claus Scheiderer, Markus Schweighofer (Konstanz) in Magdeburg, Germany.

  • Spring 2012: Didier Henrion (Toulouse) and Jerome Malick (Grenoble) are awarded the 2011 Charles Broyden prize for their paper "Projection methods for conic feasibility problems, applications to polynomial sum of squares decompositions" published in Vol. 16, Issue 1, Feb. 2011 of the journal Optimization Method Software.

  • Spring 2012: Mohab Safey El Din (Paris) joins the Institut Universitaire de France as a junior member for a duration of 5 years.

  • 11-15 June 2012: a school on hyperplane arrangements and related topics is organised by Daniele Faenzi (Pau), Vincent Florens (Pau), Daniel Matei (Bucharest) and Jean Vallès (Pau) in Pau.

  • 27-29 June 2012: Mathieu Claeys (Toulouse), PhD student working on semidefinite programming formulations for impulsive optimal control problems, is one of the 5 finalists selected for the student paper award of the American Control Conference, Montreal, Canada.

  • 3-7 September 2012: a summer school on semidefinite optimization is organised by Gabriele Nebe (Aachen) and the Research Training "Group experimental and constructive algebra" funded by the German Research Foundation in Kirchberg/Hunsrueck, Germany.

  • 17-21 September 2012: 2nd GeoLMI meeting: the Mathematics, Algorithms and Proofs (MAP) conference is organised by Thierry Coquand (Stockholm), Didier Henrion (Toulouse), Henri Lombardi (Besancon), Cordian Riener (Konstanz), Marie-Francoise Roy (Rennes) and Markus Schweighofer (Konstanz) in Konstanz, Germany. The conference includes GeoLMI sessions. See also this poster.

  • December 2012: Florian Bugarin (Toulouse) is awarded the 2012 Léopold Escande prize for his PhD thesis on computer vision applications of polynomial optimization, defended in October 2012, and co-supervised by D. Henrion (Toulouse) and Jean-José Orteu (Albi).

  • January 2013: J.-B. Lasserre (Toulouse) and J. Malick (Grenoble) are part of the new scientific board of the French CNRS working group MOA (mathematics of optimization and applications).

  • 24 February - 2 March 2013: M. Charina (Dortmund), J. B. Lasserre (Toulouse), M. Putinar (Santa Barbara) and J. Stoeckler (Dortmund), organise a workshop on structured function systems and applications at the Mathematisches Forschungsinstitut Oberwolfach (MFO), Germany.

  • 11-12 April 2013: A. Boralevi (Warsaw), D. Faenzi (Pau), E. Mezzetti (Trieste) and J. Vallès (Pau) organise a workshop on vector bundles and related topics at the University of Pau, France.

  • Summer 2013: J. Fliege (Southampton), J. B. Lasserre (Toulouse), A. N. Letchford (Lancaster) and M. Schweighofer (Konstanz), organise a thematic programme on polynomial optimisation at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.

  • 12-16 November 2013: 3rd GeoLMI meeting: D. Henrion (Toulouse) and M. Laurent (Amsterdam) organise a conference at the Centre International de Rencontres Mathématiques (CIRM) near Marseille, France.

  • 29-31 January 2014: Vector Bundles Days II: workshop organized by A. Boralevi, D. Faenzi, E. Mezzeti and J. Valles at the University of Trieste.

  • 27 February-2 March 2014: Alexander Engstroem and Cordian Riener (Helsinki) organise the ARAG workshop on applications of real algebraic geometry at Aalto University, Helsinki, Finland.

  • 6-12 April 2014: 4th GeoLMI meeting: D. Henrion (Toulouse), S. Kuhlmann (Konstanz) and V. Vinnikov (Beer-Sheva) organise a workshop on Real Algebraic Geometry with a View Toward Systems Control and Free Positivity at the Mathematisches Forschungsinstitut Oberwolfach (MFO), Germany.

  • Summer 2014: Daniele Faenzi (Pau) joins the Université de Bourgogne, Dijon as a professor.

  • Marta Abril Bucero defends her PhD thesis at INRIA Sophia-Antipolis, Nice, on 12 December 2014. Advisor: Bernard Mourrain (INRIA Sophia-Antipolis). Referees: Didier Henrion (LAAS-CNRS Univ. Toulouse), Mohab Safey El Din (Univ. Pierre et Marie Curie Paris), Markus Schweighofer (Univ. Konstanz). Committee: Mariemi Alonso (Univ. Complutense Madrid), André Galligo (Univ. Nice).

  • 22-24 June 2015: 5th and final GeoLMI meeting jointly with a workshop organized by D. Henrion (Toulouse) and M. Safey El Din (Paris) in Paris.

  • Simone Naldi defends his PhD thesis at LAAS-CNRS, Univ. Toulouse, on 24 September 2015. Advisors: Didier Henrion (LAAS-CNRS Univ. Toulouse) and Mohab Safey El Din (Univ. Pierre et Marie Curie Paris). Referees: Stéphane Gaubert (Inria Saclay and Ecole Polytechnique), Bernd Sturmfels (Univ. California at Berkeley). Committee: Bernard Mourrain (Inria Nice), Giorgio Ottaviani (Univ. Florence), Bruno Salvy (Inria Lyon and Ecole Normale Supérieure Lyon), Markus Schweighofer (Univ. Konstanz).