— 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

  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, 2018-2020) — web page
  3. ANR Project  «GEOLMI — Geometry of Linear Matrix Inequalities»  (associate member, 2012-2015) — web page