RESEARCH
— Real algebraic geometry —
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Nonnegative polynomials and sums of squares, positivity certificates
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Hyperbolic polynomials and their determinantal representations
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Spectrahedra, spectrahedral shadows and convex hulls of semialgebraic sets
— Computer algebra —
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Gröbner bases, computation of syzygy modules and ideals of points
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Polynomial systems solving, structured polynomial systems, determinantal varieties
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Exact algorithms in real algebraic geometry
— Applications —
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Semidefinite programming
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Polynomial optimization
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Quantum information
For a complete list of publications, see this page
Grants
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ANR-JCJC Project «Hyperbolic Polynomials: Algorithms, Complexity, Implementations» (Principal Investigator, 2022-2025) — web page
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PGMO Project «Hyperbolic Programming : Algorithms and Implementations» (Principal Investigator, 2018-2020) — web page
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ANR Project «GEOLMI — Geometry of Linear Matrix Inequalities» (associate member, 2012-2015) — web page
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