Dominic Searles

About Me

I am currently 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.

Together with Sami Assaf, I organize the USC Combinatorics Seminar.

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.

Submitted Preprints

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

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

12. Sami Assaf and Dominic Searles. Kohnert tableaux and a lifting of quasi-Schur functions, preprint 2016. [arxiv]

Publications

11. Oliver Pechenik and Dominic Searles. Decompositions of Grothendieck Polynomials, International Mathematics Research Notices (to appear, accepted 2017). https://doi.org/10.1093/imrn/rnx207

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

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

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

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

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

5. 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

4. 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.

3. 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.

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: dsearles (at) usc.edu
Office: KAP 424C

Department of Mathematics
University of Southern California
3620 S Vermont Ave KAP 104
Los Angeles, CA 90089-2532