Let be a polynomial or power series in several variables, or, more generally, a nonzero element in some regular commutative ring. A matrix factorization of consists of a pair of square matrices and of the same size, with entries in the given ring, such that the matrix product is multiplied by the identity matrix. For example, if is a matrix whose determinant is and is its adjoint matrix, then is a matrix factorization of .
Such matrix factorizations are nowadays ubiquitous in several different fields in physics and mathematics, including String Theory, Commutative Algebra, Algebraic Geometry, both in its classical and its noncommutative version, Singularity Theory, Representation Theory, Topology, there in particular in Knot Theory.
The workshop has brought together leading researchers and young colleagues from the various input fields; it was the first workshop on this topic in Oberwolfach. For some leading researchers from neighboring fields, this was their first visit to Oberwolfach.
Cite this article
Ragnar-Olaf Buchweitz, Kentaro Hori, Henning Krause, Christoph Schweigert, Matrix Factorizations in Algebra, Geometry, and Physics. Oberwolfach Rep. 10 (2013), no. 3, pp. 2501–2552DOI 10.4171/OWR/2013/44