STEVEN RAYAN

Associate Professor, Department of Mathematics & Statistics, University of Saskatchewan
Office 209, McLean Hall, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, CANADA



rayan (at) math.usask.ca | Dept of Math & Stats | USask


  30. Moduli spaces of generalized hyperpolygons (with L. Schaposnik) 29. Crystallography of hyperbolic lattices (with I. Boettcher, A. Gorshkov, A. Kollár, J. Maciejko, R. Thomale) 28. Toric co-Higgs bundles on toric varieties (with I. Biswas, A. Dey, M. Poddar)
  • Year | 2021
  • arXiv | math.AG/DG:2004.00730
  • Journal | Illinois J. Math. 65 (2021), no. 1, 181--190
  • DOI | 10.1215/00192082-8827663
27. Twisted cyclic quiver varieties on curves (with E. Sundbo)
  • Year | 2021
  • arXiv | math.AG/RT:1905.11508
  • Journal | Eur. J. Math. 7 (2021), no. 1, 205--225
  • DOI | 10.1007/s40879-019-00365-0
26. What is...a hyperpolygon? (with L. Schaposnik)
  • Year | 2021
  • Journal | Notices Amer. Math. Soc. 68 (2021), no. 1, 94--97
  • Download | AMS.org
  • DOI | 10.1090/noti2204
25. The Kapustin-Witten equations and nonabelian Hodge theory (with C.-C. Liu, Y. Tanaka) 24. Homogeneous Higgs and co-Higgs bundles on Hermitian symmetric spaces (with I. Biswas)
  • Year | 2019
  • arXiv | math.AG/DG:1910.12365
  • Journal | Internat. J. Math. 31 (2020), no. 14, 2050118, 20 pp.
  • DOI |10.1142/S0129167X20501189
23. Hyperbolic band theory (with J. Maciejko) 22. Nonabelian Hodge theory and vector-valued modular forms (with C. Franc)
  • Year | 2020
  • arXiv | math.NT/AG/DG:1812.06180
  • Journal | AMS Contemp. Math. 753 (2020), 95--118
  • DOI | 10.1090/conm/753/15166
21. Principal co-Higgs bundles on P1 (with I. Biswas, O. García-Prada, J. Hurtubise)
  • Year | 2020
  • arXiv | math.AG:1810.12376
  • Status | Proc. Edinb. Math. Soc. (2) 63 (2020), no. 2, 512--530
  • DOI | 10.1017/S0013091520000024
20. The Calogero-Françoise integrable system: algebraic geometry, Higgs fields, and the inverse problem (with T. Stanley, J. Szmigielski) 19. Ginzburg-Landau equations on Riemann surfaces of higher genus (with D. Chouchkov, N. Ercolani, I. M. Sigal)
  • Year | 2020
  • arXiv | math.AP/math-ph:1704.03422
  • Journal | Ann. Inst. Henri Poincaré C 37 (2020), no. 1, 79--103
  • DOI | 10.1016/j.anihpc.2019.04.002
18. Explicit Poincaré duality in the cohomology ring of the SU(2) character variety of a surface (with L. Jeffrey, A. Lindberg)
  • Year | 2019
  • arXiv | math.DG/AG/SG:2007.00196
  • Status | Accepted, to appear in Expositiones Mathematicae
  • DOI | 10.1016/j.exmath.2020.06.003
17. Hyperpolygons and Higgs bundles 16. Abstract integrable systems on hyperkähler manifolds arising from Slodowy slices (with P. Crooks) 15. Spectral curves for the triple reduced product of coadjoint orbits for SU(3) (with J. Hurtubise, L. Jeffrey, P. Selick, J. Weitsman)
  • Year | 2018
  • arXiv | math.AG/DG/SG:1708.00752
  • Journal | Geometry and Physics Vol II: A Festschrift in Honour of Nigel Hitchin (2018), 611--622
  • DOI | 10.1093/oso/9780198802020.003.0025
14. Aspects of the topology and combinatorics of Higgs bundle moduli spaces 13. Geodesics on a Kerr-Newman-(anti-)de Sitter instanton (with A. Lindberg)
  • Year | 2018
  • arXiv | math.DG/gr-qc:1805.08887
  • Journal | J. Geom. Phys. 132 (2018), 114--130
  • DOI | 10.1016/j.geomphys.2018.05.018
12. Twisted argyle quivers and Higgs bundles (with E. Sundbo)
  • Year | 2018
  • arXiv | math.AG/DG/RT:1803.04531
  • Journal | Bull. Sci. Math. 146 (2018), 1--32
  • DOI | 10.1016/j.bulsci.2018.03.003
11. A vanishing theorem for co-Higgs bundles on the moduli space of bundles (with I. Biswas) 10. The triple reduced product and Hamiltonian flows (with L. Jeffrey, G. Seal, P. Selick, J. Weitsman) 9. The quiver at the bottom of the twisted nilpotent cone on P1 8. Some results on equivariant contact geometry for partial flag varieties (with P. Crooks)
  • Year | 2016
  • arXiv | math.RT/AG/DG: 1505.03127
  • Journal | Internat. J. Math. 27 (2016), no. 8, 1650066, 13 pp.
  • DOI |10.1142/S0129167X1650066X
7. Hyperpolygons and Hitchin systems (with J. Fisher)
  • Year | 2016
  • arXiv | math.AG/SG: 1410.6467
  • Journal | Int. Math. Res. Notices IMRN (2016), no. 6, 1839--1870
  • DOI | 10.1093/imrn/rnv172
6. Introduction to nonabelian Hodge theory: flat connections, Higgs bundles, and complex variations of Hodge structure (with A. García-Raboso)
  • Year | 2015
  • arXiv | math.CV/AG/DG: 1406.1693
  • Journal | Fields Inst. Monogr. 34 (2015), 131--171
  • ISBN | 978-1-4939-2829-3
5. Constructing co-Higgs bundles on CP2
  • Year | 2014
  • arXiv | math.AG/DG: 1309.7014
  • Journal | Q. J. Math. 65 (2014), no. 4, 1437--1460
  • DOI | 10.1093/qmath/hau017
4. Co-Higgs bundles on P1
  • Year | 2013
  • arXiv | math.AG/DG: 1010.2656
  • Journal | New York J. Math. 19 (2013), 925--945
  • ISSN | 1076-9803/2013
3. Geometry of co-Higgs bundles 2. Moduli of anti-Higgs bundles over the projective line
  • Year | 2008
  • Dissertation | Transfer of Status Thesis (Oxford)
1. Particle dynamics in Kerr-Newman-de Sitter spacetimes  

You can find my works on the arXiv, INSPIRE-HEP, Google Scholar, and ORCiD.