I am a Senior Lecturer in the Department of Mathematics and Statistics at the University of Otago. Previously I was an Assistant Professor (RTPC) in the Department of Mathematics at the University of Southern California. I received my Ph.D in 2015 from the University of Illinois at Urbana-Champaign, under the direction of Alexander Yong.

My current research interests broadly involve the rich interplay between algebra, geometry and combinatorics, with a particular focus on questions of positivity in algebraic combinatorics.

27.
*Diagram supermodules for 0-Hecke-Clifford algebras*, preprint 2022.
[arxiv]

26. (with Sarah Mason)
*The "Young" and "reverse" dichotomy of polynomials*, preprint 2021.
[arxiv]

25. (with Joshua Bardwell)
*0-Hecke modules for Young row-strict quasisymmetric Schur functions*, European Journal of Combinatorics
**102** (2022), 103494, 18 pages.
[arxiv]

24. (with Sarah Mason)
*Lifting the dual immaculate functions*, Journal of Combinatorial Theory, Series A
**184** (2021), 105511, 52 pages.

23. (with Joshua Bardwell)
*Young row-strict quasisymmetric Schur functions and 0-Hecke modules*,
Séminaire Lotharingien de Combinatoire **85B** (2021), Article #68, 12 pages.

22. (with Cara Monical and Oliver Pechenik)
*Polynomials from combinatorial K-theory*,
Canadian Journal of Mathematics **73** no. 1 (2021), 29-62.

21. (with Oliver Pechenik)
*Asymmetric function theory*, In: Schubert Calculus and its Applications in Combinatorics and Representation Theory, Springer (2020), 73-112.

20.
*Indecomposable 0-Hecke modules for extended Schur functions*,
Proceedings of the American Mathematical Society **148**
(2020), 1933-1943.

19.
*Polynomial bases: positivity and Schur multiplication*,
Transactions of the American Mathematical Society **373** (2020),
819-847.

18.
*Extended Schur functions and 0-Hecke modules*,
Séminaire Lotharingien de Combinatoire **84B** (2020), Article #37, 11 pages.

17. (with Sami Assaf)
*Kohnert polynomials*, to appear in Experimental Mathematics (accepted 2019).

16. (with Oliver Pechenik)
*Decompositions of Grothendieck Polynomials*,
International Mathematics Research Notices **2019** no. 10 (2019), 3214-3241.

15. (with Sami Assaf)
*Skew polynomials and extended Schur functions*,
Séminaire Lotharingien de Combinatoire **82B** (2019), Article #31, 12 pages.

14. (with Cara Monical and Oliver Pechenik)
*K-theoretic polynomials*,
Séminaire Lotharingien de Combinatoire **82B** (2019), Article #10, 12 pages.

13. (with Oliver Pechenik)
*Deformed Cohomology of Flag Varieties*,
Mathematical Research Letters **25** no. 2 (2018), 649-657.

12. (with Sami Assaf)
*Kohnert tableaux and a lifting of quasi-Schur functions*, Journal of Combinatorial Theory, Series A **156** (2018), 85-118.

11.
*Combinatorial bases of polynomials*,
Séminaire Lotharingien de Combinatoire **80B** (2018), Article #53, 12 pages.

10. (with Sami Assaf)
*Slide polynomials*,
Séminaire Lotharingien de Combinatoire **78B** (2017), Article #11, 12 pages.

9. (with Sami Assaf)
*Schubert polynomials, slide polynomials, Stanley symmetric functions and quasi-Yamanouchi pipe dreams*,
Advances in Mathematics
**306** (2017), 89-122.

8.
*Root-theoretic Young diagrams and Schubert calculus II*,
Journal of Combinatorics **7** no. 1 (2016), 159-203.

7. (with Alexander Yong)
*Root-theoretic Young diagrams and Schubert calculus: planarity and the adjoint varieties*,
Journal of Algebra **448** (2016), 238-293.

6. (with Arkadii Slinko)
*Noncoherent initial ideals in exterior algebras,* Beiträge zur Algebra und Geometrie **56** no. 2 (2015), 759-762.

5.
*Root-theoretic Young diagrams and Schubert calculus*, Ph.D. Thesis, University of Illinois at Urbana-Champaign, Illinois, USA (2015).

4. (with Alexander Yong)
*Root-theoretic Young diagrams, Schubert calculus and Adjoint Varieties*,
DMTCS proceedings, vol. AS (2013) 493-502.

3. (with Ilya Chevyrev and Arkadii Slinko)
*On the Number of Facets of Polytopes Representing Comparative Probability Orders,*
Order **30** no. 3 (2013), 749-761.

2.
*Initial ideals in exterior algebras*, Master's Thesis, University of Auckland, New Zealand (2009).

1. (with Marston Conder and Arkadii Slinko)
*Comparative probability orders and the flip relation*,
The 5th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 07), Prague, Czech Republic (2007) 67-76.

Office: Room 220, Science III Building

Department of Mathematics and Statistics

University of Otago

730 Cumberland Street

Dunedin 9016, New Zealand