My research interests lie in alegbraic and geometric combintorics and combinatorial commutative algebra. Specficially, I am interested in:

### Publications and Preprints

#### Publications

#### To Appear

#### Submitted

Curriculum Vita (Updated November 9, 2017)

**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

- (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. - (1) A not-so-simple Lie bracket expansion (With Julie Beier)

Involve 7 (2014), no.5, 647 – 655.

- (3) Euler-Mahonian statistics and descent bases for semigroup algebras (With Benjamin Braun)

To appear in European J. Combin. - (2) Hilbert bases and lecture hall partitions

To appear in Ramanujan J. - (1) Self dual reflexive simplices with Eulerian polynomials (With Takayuki Hibi and Akiyoshi Tsuchiya)

To appear in Graphs Combin.

- (3) Level algebras and s-lecture hall polytopes (with Florian Kohl)

Submitted - (2) Flag descents and Eulerian polynomials for wreath product quotients (with Dustin Hedmark and Cyrus Hettle)

Submitted - (1) Gorenstein properties and integer decomposition properties of lecture hall polytopes (With Takayuki Hibi and Akiyoshi Tsuchiya)

Submitted

Curriculum Vita (Updated November 9, 2017)