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.