Real Algebraic Geometry With a View Toward Moment Problems and Optimization

Continuing the tradition initiated in MFO workshop held in 2014, the aim of this workshop was to foster the interaction between real algebraic geometry, operator theory, optimization, and algorithms for systems control. A particular emphasis was given to moment problems through an interesting dialogue between researchers working on these problems in finite and infinite dimensional settings, from which emerged new challenges and interdisciplinary applications

Spherical Radon transform and the average of the condition number on certain Schubert subvarieties of a Grassmannian

International audienceWe study the average complexity of certain numerical algorithms when adapted to solving systems of multivariate polynomial equations whose coefficients belong to some fixed proper real subspace of the space of systems with complex coefficients. A particular motivation is the study of the case of systems of polynomial equations with real coefficients. Along these pages, we accept methods that compute either real or complex solutions of these input systems. This study leads to interesting problems in Integral Geometry: the question of giving estimates on the average of the normalized condition number along great circles that belong to a Schubert subvariety of the Grassmannian of great circles on a sphere. We prove that this average equals a closed formula in terms of the spherical Radon transform of the condition number along a totally geodesic submanifold of the sphere

International Congress of Mathematicians: 2022 July 6–14: Proceedings of the ICM 2022

Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library