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.

#### Talk Schedule

Time | Title | Presenter | Location |

9:00am | D-branes, categories and super-potential algebras | David Berenstein | SCGP 102 |

10:00am | N/A | Break | SCGP Cafe |

10:30am | Regular super potential algebras | David Berenstein | SCGP 102 |

11:30am | Lunch | N/A | SCGP Cafe |

1:00pm | Extended Frobenius manifolds and the Kapustin-Li formula | Johannes Walcher | SCGP 102 |

2:15pm | Terminal singularities of Calabi-Yau threefolds, Milnor numbers and applications to physics | Antonella Grassi | SCGP 102 |

3:30pm | Tea | N/A | SCGP Lobby |

Time | Title | Presenter | Location |

9:00am | Kernels for Orlov’s theorem | Matthew Ballard | SCGP 102 |

10:00am | N/A | Break | SCGP Cafe |

10:30am | Categories and Filtrations | Ludmil Katzarkov | SCGP 102 |

11:30am | Lunch | N/A | SCGP Cafe |

1:00pm | Matrix factorizations in physics: a mathematical perspective | SCGP Weekly Talk: David Morrison | SCGP 102 |

2:15pm | An introduction to the hemisphere partition function | Kentaro Hori | SCGP 102 |

3:30pm | Tea | N/A | SCGP Lobby |

Time | Title | Presenter | Location |

9:00am | Matrix factorizations and free resolutions | Irena Peeva | SCGP 102 |

10:15am | Layered Resolutions | David Eisenbud | SCGP 102 |

11:15am | N/A | Break | SCGP Cafe |

11:45am | Matrix factorizations in physics: a mathematical perspective II | David Morrison | SCGP 102 |

12:45pm | Lunch | N/A | SCGP Cafe |

3:30pm | Tea | N/A | SCGP Lobby |

Time | Title | Presenter | Location |

9:00am | Monopole operators, going beyond the Auslander-Reiten quiver | Andres Collinucci | SCGP 102 |

10:00am | N/A | Break | SCGP Cafe |

10:30am | Some categorical aspects of matrix factorizations | Hailong Dao | SCGP 102 |

11:30am | Lunch | N/A | SCGP Cafe |

1:00pm | Matrix factorizations in physics: a mathematical perspective III | David Morrison | SCGP 102 |

2:15pm | Deformation theory of matrix factorizations and physics applications | Johanna Knapp | SCGP 102 |

3:30pm | Tea | N/A | SCGP Lobby |

Time | Title | Presenter | Location |

9:00am | Crepant Categorical Resolutions and a Toric Orlov Theorem | David Favero | SCGP 102 |

10:15am | F-theory on Singular Spaces | Raffaele Savelli | SCGP 102 |

11:15am | N/A | Break | SCGP Cafe |

11:45am | Matrix Factorizations and Tilting Objects | Ragnar Buchweitz | SCGP 102 |

12:45pm | Lunch | N/A | SCGP Cafe |

3:30pm | Tea | N/A | SCGP Lobby |