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Michael DiPasquale

Michael DiPasquale

Assistant Professor
Department of Math and Statistics

Education

  • University of Illinois Urbana-Champaign (UIUC), Urbana, IL
    • Ph.D., Mathematics, May 2015
    • Advisor: Professor Hal Schenck
    • Thesis: Splines on polytopal complexes
  • Wheaton College, Wheaton, IL
    • B.S., Mathematics, May 2009

Research Interests

Computational commutative algebra and algebraic geometry. Emphasis on pure and applied problems which can be approached with the tools of algebraic geometry and commutative algebra.

Publications

  • 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

  • Koszul multi-Rees algebras of principal L-Borel Ideals (with B. Jabbar Nezhad), submitted. arXiv:2008.09565

  • A lower bound for the dimension of tetrahedral splines in large degree (with N. Villamizar), submitted. arXiv:2007.12274

  • A lower bound for splines on tetrahedral vertex stars (with N. Villamizar), submitted. arXiv:2005.13043

  • On resurgence via asymptotic resurgence (with B. Drabkin), submitted. arXiv:2003.06980

  • Counting the dimension of splines of mixed smoothness: A general recipe, and its application to meshes of arbitrary topologies (with D. Toshniwal), submitted. arXiv:2001.01774

  • A homological characterization for freeness of multi-arrangements arXiv:1806.05295