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  1. ; ; ( , Selecta Mathematica)
    Matrix Schubert varieties are affine varieties arising in the Schubert calculus of the complete flag variety. We give a formula for the Castelnuovo–Mumford regularity of matrix Schubert varieties, answering a question of Jenna Rajchgot. We follow her proposed strategy of studying the highest-degree homogeneous parts of Grothendieck polynomials, which we call Castelnuovo–Mumford polynomials. In addition to the regularity formula, we obtain formulas for the degrees of all Castelnuovo–Mumford polynomials and for their leading terms, as well as a complete description of when two Castelnuovo–Mumford polynomials agree up to scalar multiple. The degree of the Grothendieck polynomial is a new permutation statistic which we call the Rajchgot index; we develop the properties of Rajchgot index and relate it to major index and to weak order. 
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    Free, publicly-accessible full text available July 3, 2025
  2. ; ( , Journal of the London Mathematical Society)
    Abstract

    In the previous work, we initiated the study of the cohomology of locally acyclic cluster varieties. In the present work, we show that the mixed Hodge structure and point counts of acyclic cluster varieties are essentially determined by the combinatorics of the independent sets of the quiver. We use this to show that the mixed Hodge numbers of acyclic cluster varieties of really full rank satisfy a strong vanishing condition.

     
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  3. ; ( , Advances in Geometry)
    Abstract We study Dressians of matroids using the initial matroids of Dress and Wenzel. These correspond to cells in regular matroid subdivisions of matroid polytopes. An efficient algorithm for computing Dressians is presented, and its implementation is applied to a range of interesting matroids. We give counterexamples to a few plausible statements about matroid subdivisions. 
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  4. ; ; ( , Selecta Mathematica)
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  5. ; ( , Proceedings of the American Mathematical Society)
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  6. ; ; ( , Journal of Commutative Algebra)
    null (Ed.)
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  7. ; ; ; ( , Algebraic Combinatorics)
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