BA, DPhil
Fellow and Tutor in Mathematics, Professor of Mathematics

Academic Background

Professor Dancer studied at Jesus College. He was awarded the Junior Mathematical Prize (for the top First in Mathematics) and the Davies Prize, and then took a DPhil under the supervision of Nigel Hitchin. He has held research fellowships at Peterhouse (Cambridge), the Max-Planck-Institut (Bonn) and IHES (Paris). He was Assistant Professor then Associate Professor at McMaster University, Canada before returning to Jesus College to take up a Fellowship.

Undergraduate Teaching

Pure Mathematics.

Postgraduate Teaching

Differential Geometry. DPhil students supervised: Brandon Dammerman (DPhil 2004), Theofanis Matsoukas (DPhil 2010), Maria Buzano (DPhil 2012), Markus Roeser (DPhil 2012), Alejandro Betancourt de la Parra (DPhil 2016), Elisabeth Grieger (PhD 2015 Kings College London : joint supervision), Matthias Wink (current), Syafiq Johar (current), Maxence Mayrand (current) and Omar Kidwai (current: joint supervision). I have also supervised five Masters dissertations.

Editorships

I was a managing editor of the Quarterly Journal of Mathematics from 2007 to 2017, and subject editor for geometry from 2002 to 2007.

Grants

Principal Investigator for EPSRC grants EP/E501958/1 and EP/J00902/1 (until April 2013).

Research Interests

Differential Geometry, especially the study of Einstein spaces. Notes for Classification of Superpotentials.

Publications

(i) Papers published in refereed journals:

1. A. Dancer. Nahm data and SU(3) monopoles. Nonlinearity 5 (1992) 1355-73.
2. A. Dancer and R. Leese. Dynamics of SU(3) monopoles. Proc. R. Soc. Lond. A 440 (1993) 421-30.
3. A. Dancer. Dihedral singularities and gravitational instantons. Journal of Geometry and Physics 12 (1993) 77-91.
4. A. Dancer. Nahm's equations and hyperkahler geometry. Communications in Mathematical Physics 158 (1993) 545-568.
5. A. Dancer and I. Strachan. Kahler-Einstein metrics with SU(2) action. Math. Proc. Camb. Phil. Soc. 115 (1994) 513-525.
6. A. Dancer. A family of hyperkahler manifolds. Quarterly Journal of Mathematics 45 (1994) 463-478.
7. A. Dancer and A. Swann. Hyperkahler metrics associated to compact Lie groups. Math. Proc. Cam. Phil. Soc. 120 (1996) 61-69.
8. A. Dancer. Scalar-flat Kahler metrics with SU(2) symmetry. J. fur Reine und Angewandte Math. 479 (1996) 99-120.
9. A. Dancer and R. Leese. A numerical study of SU(3) charge-two monopoles with minimal symmetry breaking. Phys. Lett. B 390 (1997) 252-256.
10. A. Dancer and A. Swann. Hyperkahler metrics of cohomogeneity one. Journal of Geometry and Physics 21 (1997) 218-230.
11. A. Dancer and R. Szoke. Symmetric spaces, adapted complex structures and hyperkahler structures. Quarterly Journal of Mathematics 48 (1997) 27-38.
12. A. Dancer and A. Swann. The geometry of singular quaternionic Kahler quotients. International Journal of Mathematics 8 (1997) 595-610.
13. A. Dancer and M. Wang. Kahler-Einstein metrics of cohomogeneity one. Math. Annalen 312 (1998) 503-526.
14. A. Dancer and A. Swann. Quaternionic Kahler manifolds of cohomogeneity one. International Journal of Mathematics 10 (1999) 541-570.
15. A. Dancer and M. Wang. Integrable cases of the Einstein equations. Communications in Mathematical Physics 208 (1999) 225-243.
16. A. Dancer and M. Wang. The cohomogeneity one Einstein equations from the Hamiltonian viewpoint. J. fur Reine und Angewandte Math. 524 (2000) 97-128.
17. R. Bielawski and A. Dancer. The geometry and topology of toric hyperkahler manifolds. Communications in Analysis and Geometry 8 (2000) 727-759.
18. A. Dancer and M. Wang. The cohomogeneity one Einstein equations and Painleve analysis. Journal of Geometry and Physics 38 (2001) 183-206.
19. A. Dancer and M. Wang. Ricci-flat warped products and Painleve analysis. J. Math. Physics 42 (2001) 3609-3614.
20. A. Dancer and I. A. B. Strachan. Einstein metrics on tangent bundles of spheres. Classical and Quantum Gravity 19 (2002) 4663-4670.
21. A. Dancer and M. Wang. Painleve analysis of the Ricci-flat ODEs associated with Aloff-Wallach spaces and SU(1)-bundles over Fano products. J. Math. Physics 44 (2003) 3383-3406 (special volume: "Integrability, topological solitons and beyond").
22. A. Dancer and M. Wang. Painleve expansions and the Einstein equations : the two summand case. Journal of Geometry and Physics 48 (2003) 12-43.
23. A. Dancer and M. Wang. On conserved quantities of certain cohomogeneity one Ricci-flat equations Proc. Roy. Soc. Lond. A 460 (2004) 1359-1380.
24. A. Dancer and M. Wang. Painleve expansions, cohomogeneity one metrics and exceptional holonomy. Communications in Analysis and Geometry 12 (2004) 887-926.
25. A. Dancer and M. Wang. Superpotentials and the cohomogeneity one Einstein equations. Communications in Mathematical Physics 260 (2005) 75-115.
26. A. Dancer and A. Swann. Modifying hyperkahler manifolds with circle action. Asian Journal of Mathematics 10 (2006) 815-826.
27. A. Dancer and A. Swann. Toric hypersymplectic quotients. Transactions of the American Mathematical Society 359 (2007) 1265-1284.
28. A. Dancer and M. Wang. Classification of superpotentials. Communications in Mathematical Physics 284 (2008) 583-647.
29. A. Dancer and M. Wang. Some new examples of non-Kahler Ricci solitons. Mathematical Research Letters 16 (2009) 349-363.
30. A. Dancer and M. Wang. Non-Kahler expanding Ricci solitons. International Mathematics Research Notices (2009) no.6, 1107-1133.
31. A. Dancer and A. Swann. Non-abelian cut constructions and hyperkahler modifications.  Rend. Sem. Mat. Pol. Torino 68  (2010) 157-170.
32. A. Dancer and M. Wang. On Ricci solitons of cohomogeneity one. Annals of Global Analysis and Geometry 39 (2011) 259-292.
33. A. Dancer and M. Wang. Classifying superpotentials : three summands case. Journal of Geometry and Physics 61 (2011) 675-692.
34. A. Dancer, S. Hall and M. Wang. Cohomogeneity one shrinking Ricci solitons: an analytic and numerical study. Asian Journal of Mathematics 17 (2013) 33-62.
35. A. Dancer, F. Kirwan and A. Swann. Implosion for hyperkahler manifolds. Compositio Mathematica 149 (2013) 1592-1630.
36. A. Dancer, F. Kirwan and A. Swann. Implosions and hypertoric geometry.
J. Ramanujan. Math. Soc 28A (2013) 81-122 : special issue in honour of Professor C.S. Seshadri's 80th birthday.
37. A. Dancer. F. Kirwan and A. Swann. Twistor spaces for hyperkahler implosions. J. Diff. Geometry 97 (2014) 37-77.
38. M. Buzano, A. Dancer, M. Gallaugher and M. Wang. Non-Kähler expanding Ricci solitons, Einstein metrics, and exotic cone structures. Pacific Journal of Mathematics 273 (2015) 369-394.
39. M. Buzano, A. Dancer and M. Wang. A family of steady Ricci solitons and Ricci-flat metrics. Communications in Analysis and Geometry 23 (2015) 611-638.
40. A. Dancer and F. Kirwan. A multiplicative analogue of complex-symplectic implosion. European Journal of Mathematics 1 (2015) 655--668.
41. A. Dancer, F. Kirwan and M. Roeser. Hyperkahler implosion and Nahm's equations. Communications in Mathematical Physics 342 (2016) 251-301
42. A. Betancourt de la Parra, A. Dancer and M. Wang. A Hamiltonian approach to the cohomogeneity one Ricci soliton equations and explicit examples of non-Kahler solitons. J. Math. Phys. 57 (2016).

(ii) Papers published in conference proceedings:

43. A. Dancer and I.A.B. Strachan. Cohomogeneity one Kahler metrics, in "Twistor Theory (Plymouth)" Lecture Notes in Pure and Applied Mathematics vol. 169 Marcel Dekker, New York, (1995), 9-27.
44. A. Dancer and A. Swann. The structure of quaternionic Kahler quotients, in "Geometry and Physics", edited by J.E. Andersen et al., Lecture Notes in Pure and Applied Mathematics vol. 184, Marcel Dekker, New York, (1996), 313-320.
45. A. Dancer and M. Wang. Integrability and the Einstein equations, in "Symplectic and Contact Topology : Interactions and Perspectives" Fields Institute Communications 35 (edited by Y. Eliashberg, B. Khesin, F. Lalonde) (2003), 89-101.
46. A. Dancer, H. R. Jorgensen and A. Swann. Metric geometries over the split quaternions, Rend. Sem. Mat. Pol. Torino 63.2 (2005) 119-139.
47. A. Dancer and M. Wang. Einstein equations, superpotentials and convex polytopes, in "Perspectives in Riemannian Geometry", CRM Proceedings and lecture notes vol. 40 (2006) 99-107.
48. A. Dancer and A. Swann. Hypersymplectic manifolds, in "Recent developments in pseudo-Riemannian geometry", ESI Lectures in Mathematics and Physics vol. 4 (2008) 97-112.
49. A. Dancer and M. Wang. Cohomogeneity one Ricci solitons, in Proceedings of the XIX International Fall Workshop in Geometry and Physics, Porto 2010, AIP (2011) 93-98.
50. A. Dancer. Hypersymplectic geometry, in Proceedings of the XX International Fall Workshop in Geometry and Physics, Madrid 2011, AIP (2012) 130-134.
51. A. Dancer, B. Doran, F. Kirwan and A. Swann. Symplectic and hyperkahler implosion; in Proceedings of the 2013 Arbeitstagung in memory of Friedrich Hirzebruch (eds. W. Ballmann, C. Blohmann, G. Faltings, P,. Teichner, D. Zagier) Birkhauser (2016) 81-103.
52. A. Dancer and A. Swann. Hypertoric manifolds and hyperkahler moment maps, in "Special metrics and group actions in geometry'', Proceedings of the conference in honour of Simon Salamon (Rome, 16-20 November 2015), (eds. S.Chiossi, A.Fino, E.Musso, F.Podesta, L. Vezzoni) Springer-INdAM Series vol. 23, Springer-Verlag (2017).

(iii) Survey articles:

53. A. Dancer. Hyperkahler manifolds; in "Essays on Einstein manifolds" (edited by C. LeBrun and M. Wang), Surveys in Differential Geometry VI, International Press (1999) 15-38.
54. A. Dancer. Einstein manifolds. Encyclopaedia of Mathematical Physics, Elsevier (2006) 182-189.

(iv) Edited volumes:

55. Perspectives in Riemannian geometry: proceedings of the short programme on Riemannian Geometry at the CRM Montreal in 2004: CRM Proceedings and Lecture Notes vol. 40 (2006) (Editors: V. Apostolov, A. Dancer, N. Hitchin, M. Wang).

(v) Preprints

56. A. Dancer and A. Swann. Hypertoric manifolds and hyperkahler moment maps

Links

Subject notes for courses taught at Jesus College:

See also Mathematical Institute website.