39. Topological recursion and variations of spectral curves for twisted Higgs bundles (with C. Mahadeo)

38. A generalized spectral correspondence (with K. Banerjee)

37. Kirwan surjectivity and Lefschetz-Sommese theorems for a generalized hyperkähler reduction (with J. Fisher, L. Jeffrey, A. Malusà)

36. On the hyperbolic Bloch transform (with Á. Nagy)

35. TQFTs and quantum computing (with M. Azam)

34. Hyperbolic band theory through Higgs bundles (with E. Kienzle)

33. The Kapustin-Witten equations and nonabelian Hodge theory (with C.-C. Liu, Y. Tanaka)

32. Crystallography of hyperbolic lattices (with I. Boettcher, A. Gorshkov, A. Kollár, J. Maciejko, R. Thomale)

31. Automorphic Bloch theorems for hyperbolic lattices (with J. Maciejko)

30. Quantum matter from algebraic geometry and number theory

  • Year | 2022
  • Status | Accepted, to appear in Proceedings of the Nankai Symposium on Mathematical Dialogues
  • Download | Local

29. All 81 crepants resolutions of a finite quotient singularity are hyperpolygon spaces (with G. Bellamy, A. Craw, T. Schedler, H. Weiss)

28. Explicit Poincaré duality in the cohomology ring of the SU(2) character variety of a surface (with L. Jeffrey, A. Lindberg)

  • Year | 2021
  • arXiv | math.DG/AG/SG:2007.00196
  • Journal | Expo. Math. 39 (2021), no. 3, 411--419
  • DOI | 10.1016/j.exmath.2020.06.003

27. Hyperbolic band theory (with J. Maciejko)

26. Moduli spaces of generalized hyperpolygons (with L. Schaposnik)

25. 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

24. 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

23. 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

22. Homogeneous Higgs and co-Higgs bundles on Hermitian symmetric spaces (with I. Biswas)

  • Year | 2020
  • arXiv | math.AG/DG:1910.12365
  • Journal | Internat. J. Math. 31 (2020), no. 14, 2050118, 20 pp.
  • DOI |10.1142/S0129167X20501189

21. 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

20. 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

19. The Calogero-Françoise integrable system: algebraic geometry, Higgs fields, and the inverse problem (with T. Stanley, J. Szmigielski)

18. 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

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.