Questions in computational complexity, statistical learning theory, signal processing, scientific data analysis, and other areas have recently been recast in terms of geometry and representation theory. Among them are: the complexity of matrix multiplication, Valiant's approach to P=NP, measures of entanglement in quantum information theory, matchgates in computer science, graphical models in statistical learning theory, the study of phylogenetic invariants, independent component analysis and other multilinear data analytic techniques in bioinformatics, signal processing, and spectroscopy.
The geometric perspective allows one to understand the questions in a more general mathematical context. It explains known results in terms of standard theorems in geometry and helps to advance the relevant areas.
The goals of this workshop are twofold: To introduce the relevant geometry and representation theory and to present and discuss open questions from the relevant areas that we believe could be resolved by workshop participants.
We will introduce the problems that lead to varieties in spaces of tensors and cover the basic geometry and representation theory needed to study them. By the middle of the second week we expect to begin projects working on open questions.
For more advanced participants, there will be a follow-up research workshop at the American Institute of Mathematics (AIM) the week after the graduate workshop. Information on the research workshop is available at http://www.aimath.org/ARCC/workshops/repnsoftensors.html.
If you are a student who has not been nominated for this workshop by one of our Academic Sponsors, please e-mail coord@msri.org for information about registration. |
