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)

    Period

    2011 - 2015

    Participants

  • 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, 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

    Research associates

    The project funds several PhD theses and post-doctoral fellowships. Interested candidates please contact us.

  • PhD thesis: Algorithms of real algebraic geometry for systems control and aerospace applications, co-supervised by Mohab Safey El Din (Paris) and Didier Henrion (Toulouse).

    Context

    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.

    Events

  • 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).
  • Fall 2011: a workshop is organised by Ronan Quarez (Rennes) in Rennes on 24-25 November 2011.
  • 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.
  • 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.
  • 17-21 September 2012: 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.
  • 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, Germany.
  • 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: D. Henrion (Toulouse) and M. Laurent (Amsterdam) organise a conference at the Centre International de Rencontres Mathématiques (CIRM) near Marseille, France.