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The structure of free resolutions plays an important role in analyzing singularities of varieties of low codimension. Codimension two Cohen-Macaulay varieties (resp. codimension three Gorenstein varieties) come from rank conditions on an n x (n+1) matrix (resp. a skew-symmetric (2n+1) x (2n+1) matrix). This workshop seeks to push such results to Cohen-Macaulay varieties of codimension three and Gorenstein varieties of codimension four.