Dominic Searles

About Me

I am a 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 CV can be found here.

Research

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.

Preprints

22. (with Sarah Mason) Lifting the dual immaculate functions, preprint 2020. [arxiv]

21. (with Oliver Pechenik) Asymmetric function theory, preprint 2019. [arxiv]

Publications

20. Indecomposable 0-Hecke modules for extended Schur functions, Proceedings of the American Mathematical Society, to appear.

19. (with Cara Monical and Oliver Pechenik) Polynomials from combinatorial K-theory, Canadian Journal of Mathematics, to appear.

18. Polynomial bases: positivity and Schur multiplication, Transactions of the American Mathematical Society, to appear.

17. (with Sami Assaf) Kohnert polynomials, Experimental Mathematics, to appear.

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

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

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

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

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

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

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

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

Refereed Conference Proceedings

8. (with Sami Assaf) Skew polynomials and extended Schur functions, The 31st International Conference on Formal Power Series and Algebraic Combinatorics, Ljubjlana, Slovenia (FPSAC 2019). Séminaire Lotharingien de Combinatoire, to appear, 2019.

7. (with Cara Monical and Oliver Pechenik) K-theoretic polynomials, The 31st International Conference on Formal Power Series and Algebraic Combinatorics, Ljubjlana, Slovenia (FPSAC 2019). Séminaire Lotharingien de Combinatoire, to appear, 2019.

6. Combinatorial bases of polynomials, The 30th International Conference on Formal Power Series and Algebraic Combinatorics, Hanover, NH, U.S.A. (FPSAC 2018). Séminaire Lotharingien de Combinatoire 80B (2018), Article #53, 12pp.

5. (with Sami Assaf) Slide polynomials, The 29th International Conference on Formal Power Series and Algebraic Combinatorics, London, United Kingdom (FPSAC 2017). Séminaire Lotharingien de Combinatoire 78B (2017), Article #11, 12pp.

4. (with Alexander Yong) Root-theoretic Young diagrams, Schubert calculus and Adjoint Varieties, The 25th International Conference on Formal Power Series and Algebraic Combinatorics, Paris, France (FPSAC 2013). DMTCS proceedings, vol. AS (2013) 493-502.

3. (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.

Theses

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

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

Contact Information

Email: YYYYYYdominic.searles@otago.ac.nz (delete six letters)
Office: Room 219, Science III Building

Department of Mathematics and Statistics
University of Otago
730 Cumberland Street
Dunedin 9016, New Zealand