## Matrix Factorizations in Algebra, Geometry, and Physics

 dc.date.accessioned 2019-10-24T14:45:38Z dc.date.available 2019-10-24T14:45:38Z dc.date.issued 2013 dc.identifier.uri http://publications.mfo.de/handle/mfo/3375 dc.description.abstract Let $W$ be a polynomial or power series in several variables, or, more generally, a nonzero element in some regular commutative ring. A matrix factorization of $W$ consists of a pair of square matrices $X$ and $Y$ of the same size, with entries in the given ring, such that the matrix product $XY$ is $W$ multiplied by the identity matrix. For example, if $X$ is a matrix whose determinant is $W$ and $Y$ is its adjoint matrix, then $(X, Y)$ is a matrix factorization of $W$. 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. dc.title Matrix Factorizations in Algebra, Geometry, and Physics dc.identifier.doi 10.14760/OWR-2013-44 local.series.id OWR-2013-44 local.subject.msc 81 local.subject.msc 16 local.subject.msc 14 local.subject.msc 13 local.subject.msc 18 local.sortindex 815 local.date-range 01 Sep - 07 Sep 2013 local.workshopcode 1336 local.workshoptitle Matrix Factorizations in Algebra, Geometry, and Physics local.organizers Ragnar-Olaf Buchweitz, Toronto; Kentaro Hori, Kashiwa; Henning Krause, Bielefeld; Christoph Schweigert, Hamburg local.report-name Workshop Report 2013,44 local.opc-photo-id 1336 local.publishers-doi 10.4171/OWR/2013/44 local.ems-reference Buchweitz Ragnar-Olaf, Hori Kentaro, Krause Henning, Schweigert Christoph: Matrix Factorizations in Algebra, Geometry, and Physics. Oberwolfach Rep. 10 (2013), 2501-2552. doi: 10.4171/OWR/2013/44
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