Research Interests

My research interests lie in alegbraic and geometric combintorics and combinatorial commutative algebra. Specficially, I am interested in:
  • Lattice points in rational polytopes and rational cones.
    • -Ehrhart series of rational polytopes
    • -Gorenstein and Reflexive lattice polytopes
    • -Level and Pseudo-Gorenstein lattice polytopes
    • -Computation of Hilbert bases of rational cones
    • -Triangulations of lattice polytopes
  • Graded semi-group algebras.
    • -Classification of Gorenstein and level algebras arising from rational polytopes and cones.
    • -Coinvariant algebras arrising from rational polytopes
    • -Computation and grading of minimal generating sets.
  • Integer partitions
    • -Generating function identities arising from lecture hall partitions
    • -Permutation statistics arising from lecture hall partitions
    • -Rational polytopes and cones related to lecture hall partitions
    • -Coinvariant algebras related to lecture hall partitions
  • Groebner bases for toric ideals
    • -Groebner basis techniques for triangulations of lattice polytopes
    • -Groebner basis techniques for determining bases of coinvariant algebras

Publications and Preprints

Publications

  1. (2) New families of graphs whose independence polynomials have only real zeros. (With Patrick Bahls and Elizabeth Bailey)
    Australas. J. Combin. 60 (2014), 128 – 135.
  2. (1) A not-so-simple Lie bracket expansion (With Julie Beier)
    Involve 7 (2014), no.5, 647 – 655.

To Appear

  1. (3) Euler-Mahonian statistics and descent bases for semigroup algebras (With Benjamin Braun)
    To appear in European J. Combin.
  2. (2) Hilbert bases and lecture hall partitions
    To appear in Ramanujan J.
  3. (1) Self dual reflexive simplices with Eulerian polynomials (With Takayuki Hibi and Akiyoshi Tsuchiya)
    To appear in Graphs Combin.

Submitted

  1. (3) Level algebras and s-lecture hall polytopes (with Florian Kohl)
    Submitted
  2. (2) Flag descents and Eulerian polynomials for wreath product quotients (with Dustin Hedmark and Cyrus Hettle)
    Submitted
  3. (1) Gorenstein properties and integer decomposition properties of lecture hall polytopes (With Takayuki Hibi and Akiyoshi Tsuchiya)
    Submitted

Curriculum Vita (Updated November 9, 2017)