RESEARCH


    — Real algebraic geometry —
  1. Nonnegative polynomials and sums of squares
  2. Hyperbolic polynomials and their determinantal representations
  3. Spectrahedra, spectrahedral shadows and convex hulls of semialgebraic sets

    — Computer algebra —
  1. Gröbner bases, computation of syzygy modules, polynomial interpolation
  2. Polynomial systems solving, structured polynomial systems, determinantal varieties
  3. Exact algorithms in real algebraic geometry

    — Applications —
  1. Semidefinite programming
  2. Polynomial optimization
  3. Discrete geometry



For a complete list of publications, see this page


Grants
  1. ANR-JCJC Project  «Hyperbolic Polynomials: Algorithms, Complexity, Implementations»  (Principal Investigator, 2022-2025) — web page
  2. PGMO Project  «Hyperbolic Programming : Algorithms and Implementations»  (Principal Investigator, 2018-2022) — web page
  3. ANR Project  «GEOLMI — Geometry of Linear Matrix Inequalities»  (associate member, 2012-2015) — web page