I am currently 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.

My current research relates to questions of positivity in algebraic combinatorics. It particularly concerns the problem of finding manifestly nonnegative combinatorial rules describing Schubert structure constants.

17. Cara Monical, Oliver Pechenik, Dominic Searles.
*Polynomials from combinatorial K-theory*, preprint 2018.
[arxiv]

16. Sami Assaf and Dominic Searles.
*Kohnert polynomials*, preprint 2017.
[arxiv]

15. Dominic Searles.
*Polynomial bases: positivity and Schur multiplication*, Transactions of the American Mathematical Society, to appear (accepted 2018).
[arxiv]

14. Oliver Pechenik and Dominic Searles.
*Deformed Cohomology of Flag Varieties*, Mathematical Research Letters **25** no. 2 (2018), 649-657.

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

12. Oliver Pechenik and Dominic Searles.
*Decompositions of Grothendieck Polynomials*,
International Mathematics Research Notices, rnx207, 2017.

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

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

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

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

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

6. Dominic Searles.
*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. Sami Assaf and Dominic Searles.
*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. Dominic Searles and 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. Marston Conder, Dominic Searles 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.

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

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

Office: Room 219, Science III Building

Department of Mathematics and Statistics

University of Otago

730 Cumberland Street

Dunedin 9016, New Zealand