Geometry and representation theory of tensors for computer science, statistics and other areas

July 21 to July 25, 2008

at the

American Institute of Mathematics, San Jose, California

organized by

Joseph Landsberg, Lek-Heng Lim, Jason Morton, and Jerzy Weyman

Original Announcement

This workshop will be devoted to translating questions from quantum computing, complexity theory, statistical learning theory, signal processing, and data analysis to problems in geometry and representation theory. In all these areas varieties in spaces of tensors invariant under linear changes of coordinates appear as central objects of study. Despite their different origins, there are striking similarities among the relevant varieties and this workshop will study ways of approaching questions such as finding defining equations, hidden symmetries, and singularities.

The main topics for the workshop are

  1. Geometric approaches to P?=NP
  2. Algebraic statistics, particularly hidden variable models
  3. Multi-linear techniques in data analysis and signal processing
  4. Entanglement in quantum information theory
By the end of the workshop, researchers in the relevant areas will be up to date on what is known about their questions from a geometric perspective and geometers will have a list of open questions to work on. We hope this workshop is the beginning of collaborations between mathematicians and researchers in the targeted areas.

This workshop is a followup to an MSRI program with the same title.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A detailed summary of the mathematical activities during the workshop, by Luke Oeding.

Papers arising from the workshop:

On spinor varieties and their secants
by  Laurent Manivel
On rectangular Kronecker coefficients
by  Laurent Manivel
A note on certain Kronecker coefficients
by  Laurent Manivel
Graph homomorphisms with complex values: A Dichotomy Theorem
by  Jin-Yi Cai, Xi Chen, and Pinyan Lu
An overview of mathematical issues arising in the geometric complexity theory approach to VP v.s. VNP
by  Peter Buergisser, J. M. Landsberg, Laurent Manivel, and Jerzy Weyman
Holographic algorithms without matchgates
by  J. M. Landsberg, Jason Morton, and Serguei Norine
Kruskal's theorem
by  J. M. Landsberg
On the ranks and border ranks of symmetric tensors
by  J. M. Landsberg and Zach Teitler