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Abstract: The famous Gromov-Vershik metric measure space reconstruction theorem gives a way to reconstruct uniquely the metric measure space (up to a measure preserving isometry) by a suitable information on distances between randomly chosen points in the latter. The natural questions are then what can be reconstructed from the spectral information on random distance matrices. We will discuss some of these problems and their relationship to the multidimensional scaling, a widely used method in manifold learning.
Bio: Professor Eugene Stepanov is an outstanding expert in metric geometry and geometric measure theory with a broad range of applications, in particular in control, dynamical systems and calculus of variations. Having obtained the PhD. degree in 1999, by Scuola Normale Superiore, Pisa, Italy, he obtained the Doctor of Sciences (equivalent to Habilitation in France or Germany), from Institute of Information Transmission problems, Moscow, Russian Federation in 2006.
He has worked as a professor at the Department of Mathematical Physics of Saint Petersburg State University. Nowadays, he works at University of Pisa, combining this with a position at Saint Petersburg Department of Steklov Institute.
