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- Title: Introductory talk on Polynomial Optimization and Lasserre hierarchies
Speaker: Igor Klep
Date and time: Monday, February 10, 2025, at 14h15
- Title: The Christoffel function: applications, connections & extensions
Speaker: Jean Bernard Lasserre
Date and Time: Monday, February 17, 2025, at 14h15
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.
- Next Speakers:
Monique Laurent (Week of April 7 or 14, 2025)
Antonio Acin (Week of May 19, 2025)
Hamza Fawzi (Early September 2025)
