Seminars

For registration to seminars, please visit the registration page.
Online participation via this link.

Upcoming Talks

  • Title: Certified Many-Body Physics
    Speaker: Antonio Acin
    Date and time: Thursday, May 22, 2025, at 14h00
    Location: CPHT, Ecole Polytechnique, Room Luis Michel

    Abstract: When studying many-body systems, two approaches have been considered so far: analytical derivations and variational methods. The first provide exact results, as they do not involve any approximations, but scale exponentially with the number of particles, while the second scale much better but only provide estimates with no theoretical guarantees. Polynomial optimisation methods offer an alternative approach somehow combining the advantage of exact and variational methods: it provides rigorous results, now in the form of upper and lower bounds, in a scalable way. We illustrate this new approach in two paradigmatic many-body problems: the estimation of expectation values in ground states of Hamiltonian operators and in steady states of quantum open systems.
  • Video: link
  • Title: The Navascués, Pironio, Acín (NPA) hierarchy and its applications to condensed matter
    Speaker: Igor Klep
    Date and time: Thursday, April 24, 2025, at 14h00
    Location: CPHT, Ecole Polytechnique, Room Luis Michel

    Abstract: Noncommutative polynomial optimization (NPO) deals with optimization problems involving polynomial functions of variables that do not commute, typically represented as operators or matrices. Such problems naturally arise in condensed matter physics (e.g., estimating ground state energies of quantum many-body systems), quantum information theory (e.g., bounding entanglement measures), quantum chemistry (e.g., approximating molecular energy levels), and operator theory (e.g., solving noncommutative problems involving matrix inequalities).
    In this talk, I shall present the Navascués-Pironio-Acín (NPA) hierarchy, a powerful method that provides a converging sequence of semidefinite programming (SDP) relaxations for solving NPO problems. By encoding moment constraints of noncommuting operators, the NPA hierarchy yields tractable and systematically improvable bounds, with convergence guarantees to the true optimum. This makes it a valuable tool for tackling optimization problems in quantum physics and beyond.
  • Video: link

Past Talks

  • Title: Approximations for polynomial optimization on the sphere and quantum de Finetti theorems
    Speaker: Monique Laurent
    Date and time: Monday, April 7, 2025, at 14h15
    Location: Alan Turing Building – Amphithéâtre Sophie Germain

    Abstract: We revisit two approximation hierarchies for polynomial optimization on the unit sphere, whose convergence analysis for the r-th level bound was shown to be, respectively, in O(1/rˆ2) by Fang and Fawzi (in 2020, using the polynomial kernel method) and in O(1/r) by Lovitz and Johnston (in 2023, using a quantum de Finetti theorem of Christandl et al. (2007) for complex matrices with Bose symmetry).
    We investigate links between these approaches, in particular, via duality of moments and sums of squares. In particular, we propose another proof for the analysis of the spectral bounds of Lovitz and Johnston, via a “banded” real de Finetti theorem for real Bose symmetric matrices, and we show that the spectral bounds cannot have a convergence rate better than O(1/rˆ2). In addition, we show how to use the polynomial kernel method to obtain a de Finetti type result for real maximally symmetric matrices, improving an earlier result of Doherty and Wehner (2013).
    Joint work with Alexander Taveira Blomenhofer, University of Copenhagen.
  • Video: link
  • Title: The Christoffel function: applications, connections & extensions
    Speaker: Jean Bernard Lasserre
    Date and Time: Monday, February 17, 2025, at 14h15
    Location: Alan Turing Building – Amphithéâtre Sophie Germain

    Abstract: We will give a brief introduction to the Christoffel function (CF). One reason and motivation for considering this tool is that, surprisingly, although it has been known for a long time in approximation theory and orthogonal polynomials, it is only recently that its remarkable properties have proven to be very useful in analysis and data mining; for example, for support inference, outlier detection, and density approximation.
    But additionally:
    – A non-standard use of the CF allows for the interpolation of discontinuous functions without the -Gibbs phenomenon.
    – A modification (or regularization) of the CF also allows for the asymptotic approximation of the unknown density of the measure associated with the CF, avoiding the appearance of the equilibrium measure of the support (which is generally unknown).
    Finally, we will conclude by revealing some connections of the CF with apparently unrelated fields, e.g., certificates of positivity in real algebraic geometry, the Pell polynomial equation, and the equilibrium measure of a compact.
    Video: link
  • Title: Introductory talk on Polynomial Optimization and Lasserre hierarchies
    Speaker: Igor Klep
    Date and time: Monday, February 10, 2025, at 14h15
    Location: Alan Turing Building – Amphithéâtre Sophie Germain
    Video: link

Planned Talks

  • Hamza Fawzi (Early September 2025)
  • William Slofstra (Early September 2025)

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