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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.

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