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  1. ; ; (, Forum of Mathematics, Sigma)
    Abstract This paper extends the results of Boij, Eisenbud, Erman, Schreyer and Söderberg on the structure of Betti cones of finitely generated graded modules and finite free complexes over polynomial rings, to all finitely generated graded rings admitting linear Noether normalizations. The key new input is the existence of lim Ulrich sequences of graded modules over such rings. 
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  2. ; (, Proceedings of the American Mathematical Society)
    Buchweitz-Greuel-Schreyer conjectured in 1987 a lower bound on the ranks of matrix factorizations over certain local hypersurface rings [Invent. Math. 88 (1987), pp. 165–182]. We study a graded version of this conjecture, and we show that it implies a novel conjecture concerning the cohomology of sheaves over non-Fano projective hypersurfaces. 
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    Free, publicly-accessible full text available August 1, 2026
  3. ; (, Duke Mathematical Journal)
    Free, publicly-accessible full text available February 1, 2026
  4. ; ; ; (, Communications of the American Mathematical Society)
    Over a Cohen-Macaulay local ring, the minimal number of generators of a maximal Cohen-Macaulay module is bounded above by its multiplicity. In 1984 Ulrich [Math. Z. 188 (1984), pp. 23–32] asked whether there always exist modules for which equality holds; such modules are known nowadays as Ulrich modules. We answer this question in the negative by constructing families of two dimensional Cohen-Macaulay local rings that have no Ulrich modules. Some of these examples are Gorenstein normal domains; others are even complete intersection domains, though not normal. 
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    Free, publicly-accessible full text available January 1, 2026
  5. ; (, Annals of K-Theory)
    Free, publicly-accessible full text available January 1, 2026
  6. ; (, Annals of K-Theory)
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  7. ; (, Journal of Algebra)
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