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Dr Dominic Searles

(PhD University of Illinois)Generic Silhouette

Senior Lecturer

Office: Science III, room 220
Tel +64 3 479 7762
Email dominic.searles@otago.ac.nz

About

I am a Senior Lecturer in the Department of Mathematics and Statistics. I received my Ph.D in 2015 from the University of Illinois at Urbana-Champaign in 2015.

Teaching responsibilities

My teaching responsibilities include:

  • MATH 130 Fundamentals of Modern Mathematics 1
  • MATH 202 Linear Algebra
  • MATH 342 Modern Algebra
  • MATH 4AC
  • MATH 4AL Advanced Algebra

Research Interests

Algebra and Combinatorics.

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Publications

Bardwell, J., & Searles, D. (2022). 0-Hecke modules for Young row-strict quasisymmetric Schur functions. European Journal of Combinatorics, 102, 103494. doi: 10.1016/j.ejc.2021.103494

Assaf, S., & Searles, D. (2022). Kohnert polynomials. Experimental Mathematics, 31(1), 93-119. doi: 10.1080/10586458.2019.1588180

Mason, S., & Searles, D. (2021). Lifting the dual immaculate functions. Journal of Combinatorial Theory, Series A, 184, 105511. doi: 10.1016/j.jcta.2021.105511

Monical, C., Pechenik, O., & Searles, D. (2021). Polynomials from combinatorial K-theory. Canadian Journal of Mathematics / Journal canadien de mathématiques, 73(1), 29-62. doi: 10.4153/S0008414X19000464

Pechenik, O., & Searles, D. (2020). Asymmetric Function Theory. In J. Hu, C. Li & L. C. Mihalcea (Eds.), Schubert Calculus and Its Applications in Combinatorics and Representation Theory: Springer Proceedings in Mathematics & Statistics (Vol. 332). (pp. 73-112). Singapore: Springer. doi: 10.1007/978-981-15-7451-1_5

Assaf, S., & Searles, D. (2022). Kohnert polynomials. Experimental Mathematics, 31(1), 93-119. doi: 10.1080/10586458.2019.1588180

Journal - Research Article

Bardwell, J., & Searles, D. (2022). 0-Hecke modules for Young row-strict quasisymmetric Schur functions. European Journal of Combinatorics, 102, 103494. doi: 10.1016/j.ejc.2021.103494

Journal - Research Article

Mason, S., & Searles, D. (2021). Lifting the dual immaculate functions. Journal of Combinatorial Theory, Series A, 184, 105511. doi: 10.1016/j.jcta.2021.105511

Journal - Research Article

Monical, C., Pechenik, O., & Searles, D. (2021). Polynomials from combinatorial K-theory. Canadian Journal of Mathematics / Journal canadien de mathématiques, 73(1), 29-62. doi: 10.4153/S0008414X19000464

Journal - Research Article

Searles, D. (2020). Indecomposable 0-Hecke modules for extended Schur functions. Proceedings of the American Mathematical Society, 148(5), 1933-1943. doi: 10.1090/proc/14879

Journal - Research Article

Searles, D. (2020). Polynomial bases: Positivity and Schur multiplication. Transactions of the American Mathematical Society, 373(2), 819-847. doi: 10.1090/tran/7670

Journal - Research Article

Pechenik, O., & Searles, D. (2019). Decompositions of Grothendieck polynomials. International Mathematics Research Notices, 2019(10), 3214-3241. doi: 10.1093/imrn/rnx207

Journal - Research Article

Pechenik, O., & Searles, D. (2018). Deformed cohomology of flag varieties. Mathematical Research Letters, 25(2), 649-657. doi: 10.4310/MRL.2018.v25.n2.a15

Journal - Research Article

Assaf, S., & Searles, D. (2017). Schubert polynomials, slide polynomials, Stanley symmetric functions and quasi-Yamanouchi pipe dreams. Advances in Mathematics, 306, 89-122. doi: 10.1016/j.aim.2016.10.015

Journal - Research Article

Searles, D. (2016). Root-theoretic Young diagrams and Schubert calculus II. Journal of Combinatorics, 7(1), 159-203. doi: 10.4310/JOC.2016.v7.n1.a7

Journal - Research Article

Searles, D., & Yong, A. (2016). Root-theoretic Young diagrams and Schubert calculus: Planarity and the adjoint varieties. Journal of Algebra, 448, 238-293. doi: 10.1016/j.jalgebra.2015.09.039

Journal - Research Article

Searles, D., & Slinko, A. (2015). Noncoherent initial ideals in exterior algebras. Beiträge zur Algebra und Geometrie, 56(2), 759-762. doi: 10.1007/s13366-015-0239-5

Journal - Research Article

Chevyrev, I., Searles, D., & Slinko, A. (2013). On the number of facets of polytopes representing comparative probability orders. Order, 30(3), 749-761. doi: 10.1007/s11083-012-9274-0

Journal - Research Article

Pechenik, O., & Searles, D. (2020). Asymmetric Function Theory. In J. Hu, C. Li & L. C. Mihalcea (Eds.), Schubert Calculus and Its Applications in Combinatorics and Representation Theory: Springer Proceedings in Mathematics & Statistics (Vol. 332). (pp. 73-112). Singapore: Springer. doi: 10.1007/978-981-15-7451-1_5

Conference Contribution - Published proceedings: Full paper

Assaf, S., & Searles, D. (2017). Slide polynomials. Séminaire Lotharingien de Combinatoire, 78B, #11. [Full Paper]

Conference Contribution - Published proceedings: Full paper

Searles, D., & Yong, A. (2013). Root-theoretic Young diagrams, Schubert calculus and adjoint varieties. DMTCS Proceedings, AS, (pp. 493-502). Retrieved from https://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/index.html

Conference Contribution - Published proceedings: Full paper

Searles, D. (2018). Fundamental slide polynomials and their applications. Proceedings of the New Zealand Mathematical Society Colloquium. (pp. 32). Retrieved from http://nzmathsoc.org.nz/colloquium2018

Conference Contribution - Published proceedings: Abstract

Assaf, S., & Searles, D. (2017). Kohnert polynomials. arXiv. Retrieved from https://arxiv.org/abs/1711.09498

Working Paper; Discussion Paper; Technical Report

Assaf, S., & Searles, D. (2017). Kohnert tableaux and a lifting of quasi-Schur functions (v2). arXiv. Retrieved from https://arxiv.org/abs/1609.03507v2

Working Paper; Discussion Paper; Technical Report

Searles, D. (2017). Polynomial bases: Positivity and Schur multiplication. arXiv. Retrieved from https://arxiv.org/abs/1707.01172

Working Paper; Discussion Paper; Technical Report

Pechenik, O., & Searles, D. (2014). Deformed cohomology of flag varieties. arXiv. Retrieved from https://arxiv.org/abs/1410.8070

Working Paper; Discussion Paper; Technical Report

Searles, D. (2018, August). Comparative probability orders and noncoherent initial ideals of exterior algebras. Mathematics Seminar Series, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand. [Department Seminar].

Other Research Output

Searles, D. (2018, May). Kohnert polynomials. Mathematics Seminar Series, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand. [Department Seminar].

Other Research Output

Searles, D. N. (2015). Root-theoretic Young diagrams and Schubert calculus (PhD). University of Illinois, Champaign, IL. Retrieved from http://hdl.handle.net/2142/87992

Awarded Doctoral Degree

More publications...