Matrix Factorizations in Mathematics and Physics: June 12-16, 2017

Organized By: David Eisenbud, David Morrison, Irena Peeva

Workshop ScheduleAttendee List Danfords Inn Shuttle ScheduleVideos

A matrix factorization of an element w in a polynomial or power series ring (more generally, in a local or graded regular commutative ring) is a pair of square matrices (A, B) of the same size such that AB = BA = wE, where E is an identity matrix.

Matrix factorizations were introduced by Eisenbud in 1980, in order to describe the eventual structure of minimal free resolutions over hypersurfaces. Since then they have been used by mathematicians in the study of such diverse constructions as cluster tilting, Cohen-Macaulay modules, Hodge theory, Khovanov-Rozansky homology, moduli of curves, quiver and group representations, singularity theory and singularity categories and mirror symmetry.

Following ideas of Kapustin-Li and Kontsevich, physicists have used Matrix Factorizations to represent D-branes in the Landau-Ginzburg phase of a Calabi-Yau compactification. Matrix Factorizations provide supersymmetric boundary conditions for Landau-Ginzburg theories. They are also useful in describing objects of the category of D-branes related to superpotentials in Landau-Ginzburg theories, and as a tool in the theory of noncommutative crepant resolutions of singularities.

New applications of matrix factorizations are still developing quickly, and there has been a surge in interest in the field. The workshop has as its purpose to bring together the communities of those in mathematics and physics who are interested in matrix factorizations to share their techniques and problems, and to explore the newest developments.