Research

Research Interests

My research interests lie in alegbraic and geometric combintorics and combinatorial commutative algebra. In particular, I am interested in questions arising from lattice point enumeration for rational polyhedra. 

Research Articles

Publications

1. Multivariate polynomials for generalized permutohedra, (with Eric Katz) Ars Math. Contemp. 22 (2022), no. 4,  Paper No. 2, 19pp. (ArXiv Link)

2. Lattice polytopes from Schur and symmetric Grothendieck polynomials, (with Margaret Bayer, Bennet Goeckner, Su Ji Hong, Tyrrell McAllister, Casey Pinckney, Julianne Vega, and Martha Yip) Electron. J. Combin. 28 (2021), no. 2.45, 36pp. (ArXiv Link)

3. Level algebras and s-lecture hall polytopes. (with Florian Kohl) Electron. J. Combin. 27 (2020), no. 3.50, 23pp. (ArXiv Link)

4. Unconditional reflexive polytopes . (with Florian Kohl and Raman Sanyal) Discrete Comput. Geom. 64 (2020), no. 2, 427--452. (ArXiv Link) 

5. Gorenstein properties and integer decomposition properties of lecture hall polytopes. (with Takayuki Hibi and Akiyoshi Tsuchiya) Mosc. Math. J. 18 (2018), no. 4, 667--679. (ArXiv Link)

6. Hilbert bases and lecture hall partitions. Ramanujan J.  47 (2018), no.3, 509--531. (ArXiv Link)

7. Euler-Mahonian statistics and descent bases for semigroup algebras. (with Benjamin Braun) European J. Combin. 69 (2018), 237--254. (ArXiv Link)

8. Self dual reflexive simplices with Eulerian polynomials. (with Takayuki Hibi and Akiyoshi Tsuchiya) Graphs Combin. 33 (2017), no. 6, 1401-–1404.  (ArXiv Link)

9. New families of graphs whose independence polynomials have only real zeros. (with Patrick Bahls and Elizabeth Bailey) Australas. J. Combin. 60 (2014), 128--135.

10. A not-so-simple Lie bracket expansion. (with Julie Beier) Involve 7 (2014), no. 5, 647--655.

To Appear

1. Ehrhart Limits. (with Benjamin Braun) To appear in Ars Math Contemp.

Submitted

1. Flag descents and Eulerian polynomials for wreath product quotients. (with Dustin Hedmark and Cyrus Hettle) Preprint.

Survey Articles

1. Polyhedral geometry for lecture hall partitions.  Algebraic and Geometric Combinatorics on Lattice Polytopes:  Proceedings of the Summer Workshop on Lattice Polytopes (2019), 330--353. (arXiv Link)