Skoltech Colloquium: Numerical Algorithms for High-Dimensional Problems, 30.01.2014

January 30, 2014

Numerical Algorithms for High-Dimensional Problems
Speaker: Ivan Oseledets, Associate Professor at the Skolkovo Institute of Science of Technology (Skoltech). He previously was a Senior Researcher in the Institute of Numerical Mathematics of Russian Academy of Sciences (INM RAS) in Moscow, Russia (till 2013, from 2013-part time). Ivan has received the PhD degree in Numerical Mathematics from the INM RAS in 2007 and the degree of Doctor of Sciences (second Russian degree) in 2012. Ivan was an invited Professor in the Haussdorf Institute of Mathematics in Bonn in 2011, and also has a part-time position in the Max-Planck Institute for Mathematics in the Sciences (Leipzig) from 2009. Dr. Oseledets research interests include numerical analysis, linear algebra, tensor methods and their applications in high-dimensional problems: solution of PDEs, quantum chemistry and computational material design, stochastic partial differential equations, wavelets, data mining and compression. Dr. Oseledets has received the medal of Russian academy of Sciences for the best student work in Mathematics in 2005; the medal of Russian academy of Sciences for the best work among young mathematicians in 2009. He is the winner of the Dynasty Foundation contest among young mathematicians in Russia in 2012.

Abstract: Multidimensional problems are notoriously difficult due to the curse of dimensionality. However, high-dimensional problems are usually the most interesting ones and moreover, if the problem is of a considerable practical interest, often there is a method that solves it. The most vivid example is the Schrodinger equation in quantum chemistry, where efficient solution methods have been proposed. However, such methods are usually problem-specific, require a lot of efforts to implement and difficult to be applied in other areas. In the recent years, active development of mathematical foundations for the algorithms for the solution of high-dimensional problem has begun. Novel tensor formats (Hierarchical Tucker, Tensor Train) as well as surprinsing connections with other research areas (MPS, PEPS, tensor networks, graphical models) form a new research area with new fascinating theoretical and algorithmic problems and new applications in chemistry, biology and data-mining and global optimization.

Видео Skoltech Colloquium: Numerical Algorithms for High-Dimensional Problems, 30.01.2014 канала Skoltech