PhIQuS is excited to welcome Professor Igor Klep and Doctor Matthias Schotz, who will be visiting Ecole Polytechnique during two periods: February to September 2025 and January to March 2026.

Igor Klep is an expert in operator theory and real algebraic geometry, with a particular focus on semidefinite relaxations of polynomial optimization problems, both commutative and noncommutative. This branch of convex optimization gained prominence in the early 2000s, following the pioneering works of Jean-Bernard Lasserre, Pablo Parrilo, and Monique Laurent, which led to the development of the Lasserre-Parrilo hierarchy. For noncommutative problems, a parallel methodology emerged in quantum information theory through the works of Antonio Acin and collaborators in 2008.

Matthias Schotz is a mathematician working mostly on operator algebras, with a focus on the order properties of (in general unbounded) *-algebras of operators. Such algebras appear naturally as algebras of observables of physical systems, with the order given by evaluation on states: An element of the observable algebra is positive iff it gives a positive result when evaluated on any state. For classical systems, the observable algebra is commutative, and the corresponding mathematical theory that deals with such structures is real algebraic geometry, i.e. the theory of (pre- or partially) ordered commutative rings like e.g. polynomials on algebraic sets. For quantum systems, the observable algebra is noncommutative, and therefore has to be dealt with methods of a “noncommutative” real algebraic geometry, the theory of (pre- or partially) ordered -algebras like e.g. the Weyl algebra, or C-algebras.

We are thrilled to host Igor and Matthias and look forward to the exciting research, discussions, and events he will bring to our group.

Igor Klep is invited through the Gaspard Monge Visiting Professor program which supports internationally renowned scientists, enabling them to conduct research, lead workshops, and organize summer schools. This visiting Professor program provides experienced researchers with the opportunity to spend several months at an École Polytechnique laboratory, collaborating with research teams and offering students a fresh perspective through specialized teaching.

Do not hesitate to send an email to Igor to organize scientific discussions!