Optimal Transport between algebraic hypersurfaces
speaker: Fabio Cavalletti (Università degli Studi di Milano)abstract: What is the optimal way to deform a projective hypersurface into another one? We will answer this question adopting the point of view of measure theory, introducing the optimal transport problem between complex algebraic projective hypersurfaces. First, a natural topological embedding of the space of hypersurfaces of a given degree into the space of measures on the projective space is constructed. Then, the optimal transport problem between hypersurfaces is defined through a constrained dynamical formulation, minimizing the energy of absolutely continuous curves which lie on the image of this embedding. In this way an inner Wasserstein distance on the projective space of homogeneous polynomials is introduced. We will show the main properties of this distance and discuss applications on the regularity of the zeroes of a family of multivariate polynomials and on the condition number of polynomial systems solving.
timetable:
Mon 2 Dec, 11:10 - 11:55, Aula Dini
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