Publications

• Geometric aspects of the Jacobian of a hyperplane arrangement (with J. Sidman and W. Traves), Int. Math. Res. Not. IMRN (2025), no. 13, rnaf172. arXiv:2209.04929 .
• Restriction and extension for planar splines on triangulations, in Lanini, Manni, and Schenck, editors, Approximation Theory and Numerical Analysis meet Algebra, Geometry, Topology, Springer INdAM Series 60 (2024), 149-172. Springer Nature Link page
• Planar splines on a triangulation with a single totally interior edge (with B. Yuan), SIAM J. Appl. Algebra Geom. 8 (2024), no. 3, 686–712. arXiv:2306.16825
• A lower bound for the dimension of tetrahedral splines in large degree (with N. Villamizar), Constr. Approx. 59 (2024), no. 1, 1–30. arXiv:2007.12274
• Duality for asymptotic invariants of graded families (with T. Nguyen and A. Seceleanu), Adv. Math. 430 (2023), Paper No. 109208, 47 pp. arXiv:2208.11110
• Quasi-polynomial growth of numerical and affine semigroups with constrained gaps (with B. Gillespie and C. Peterson), Semigroup Forum 107 (2023), no. 1, 60–78. arXiv:2208.09760
• A homological characterization for freeness of multi-arrangements, Math. Ann. 385 (2023), no. 1-2, 745–786. arXiv:1806.05295
• On resurgence via asymptotic resurgence (with B. Drabkin), J. Algebra. 587 (2021), 64-84. arXiv:2003.06980
• Koszul multi-Rees algebras of principal L-Borel Ideals (with B. Jabbar Nezhad), J. Algebra. 581 (2021), 353-385. arXiv:2008.09565
• A lower bound for splines on tetrahedral vertex stars (with N. Villamizar), SIAM J. Appl. Algebra Geom. 5 (2021), no. 2, 250-277. arXiv:2005.13043
• Counting the dimension of splines of mixed smoothness: A general recipe, and its application to meshes of arbitrary topologies. (with D. Toshniwal), Adv. Comput. Math. (2021) arXiv:2001.01774
• On the apolar algebra of a product of linear forms (with Z. Flores and C. Peterson). In Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, ISSAC `20, pages 130-137, New York, NY, USA, 2020. Association for Computing Machinery, doi:10.1145/3373207.3404014. arXiv:2002.04818
• A Generalization of Wilf's Conjecture for Generalized Numerical Semigroups (with C. Cisto, G. Failla, Z. Flores, C. Peterson, and R. Utano), Semigroup Forum (2020), doi: 10.1007/s00233-020-10085-7 . arXiv:1909.13120
• Bivariate Semialgebraic Splines (with F. Sottile), J. Approx. Theory 254 (2020), 105392, 19 pp. arXiv:1905.08438
• Free and non-free multiplicities on the A3 arrangement (with C. Francisco, J. Mermin, and J. Schweig), J. Algebra 544 (2020), 498-532. arXiv:1609.003377
• Asymptotic resurgence via integral closures (with C. Francisco, J. Mermin, and J. Schweig), Trans. Amer. Math. Soc. 147 (2019) doi:10.90/tran/7835, arXiv:1808.01547
• The Rees Algebra of a two-Borel Ideal is Koszul (with C. Francisco, J. Mermin, J. Schweig, and G. Sosa), Proc. Amer. Math. Soc. 147 (2019), no. 2, 467-479. arXiv:1706.07462
• Free Multiplicities on the Moduli of X3 (with M. Wakefield), J. Pure Appl. Algebra 222 (2018), no. 11, 3345-3359. arXiv:1707.03961
• Inequalities for free multi-braid arrangements, Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 4, 36-41. arXiv:1705.02409
• Semialgebraic Splines (with F. Sottile and L. Sun), Comput. Aided Geom. Design 55 (2017), 26-47. arXiv:1604.05947
• Dimension of Mixed Splines on Polytopal Cells, to appear in Math. Comp. arXiv:1411.2176
• Generalized Splines and Graphic Arrangements, J. Algebraic Combin. (2016), 1-19. arXiv:1606.03091
• Associated Primes of Spline Complexes, J. Symb. Comput. (2016), 10.1016/j.jsc.2016.01.004. arXiv:1410.6894
• Lattice-Supported Splines on Polytopal Complexes, Adv. in Appl. Math. 55 (2014) 1-21. arXiv:1312.3294
• Shellability and Freeness of Continuous Splines, J. Pure Appl. Algebra 216,no. 11, 2519-2523 (2012).
• Asymptotic Connectivity of Hyperbolic Planar Graphs (with Patrick Bahls), Discrete Math. 310 no. 24, 3462-3472 (2010).
• On the Order of a Group Containing Nontrivial Gassmann Equivalent Subgroups, Rose-Hulman Undergraduate Mathematics Journal, 10 no. 1 (2009). pdf

Under Review

• Asymptotic Resurgence of Facet ideals of Graphic Matroids (with L. Fouli and A. Kumar), submitted. arXiv:2607.26294
• Trivariate Splines on Fans of Hyperplane Arrangements and Koszul Homology (with C. Checa, P. Maz\'on, T. T. Nguyen, L. Sega, P. Udanshive, A. Van Tuyl, and N. Villamizar), submitted. arxiv:2606.18298
• Algebraic geometry, Bernstein-B\'ezier analysis, and multivariate spline spaces (with P. Alfeld, M. Sirvent, T. Sorokina, N. Villamizar, W. Whiteley, and B. Yuan), submitted.
• Asymptotic Resurgence of facet and Stanley-Reisner ideals of matroids (with L. Fouli and A. Kumar), submitted. arXiv:2607.20892
• Projective curves passing through finite sets and rank decompositions of symmetric tensors (with C. Bocci, L. Chiantini, A. Mazzon, and C. Peterson), submitted.
• Generalized Hamming weights and symbolic powers of Stanley-Reisner ideals of matroids (with L. Fouli, A. Kumar, and S. Tohaneanu), submitted. arXiv:2406.13658 .