Dominic Searles

About Me

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.

Research

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.

Preprints

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

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

14. Dominic Searles. Polynomial bases: positivity and Schur multiplication, preprint 2017. [arxiv]

Publications

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. [arxiv]

12. Oliver Pechenik and Dominic Searles. Decompositions of Grothendieck Polynomials, International Mathematics Research Notices, rnx207, 2017. https://doi.org/10.1093/imrn/rnx207

11. Oliver Pechenik and Dominic Searles. Deformed Cohomology of Flag Varieties, Mathematical Research Letters (to appear, accepted 2017). [arxiv]

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

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

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

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

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

Refereed Conference Proceedings

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.

Theses

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).

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