I'm a fourth year PhD student at the University of Cambridge. My supervisor is Julius Ross. I was previously an undergraduate of Trinity College, Dublin. I'm a member of its sister college in Cambridge, St. John's.
From February to August 2016 I will be a Fondation Wiener - Anspach scholar at the Université libre de Bruxelles, visiting Joel Fine's group.
Starting in October 2016, I will be a Research Fellow at Gonville & Caius College, Cambridge.
My first name is pronounced "Rui" (it's Irish).
I am a complex geometer. I'm interested in the existence of certain canonical Kähler metrics (e.g. Kähler-Einstein and constant scalar curvature) and notions of algebro-geometric stability (e.g. K-stability). The link between the two is the so-called "Yau-Tian-Donaldson" conjecture, which motivates my work.
My CV. My email address is rd430(at)cam.ac.uk.
Geometry Tea 2013-2014, 2014-2015 and 2015-2016.
Papers and preprints:
- K-stability for Kähler manifolds (joint with Julius Ross) arXiv:1602.08983
- A finite dimensional approach to Donaldson's J-flow (joint with Julien Keller) arXiv:1507.03461
- On K-stability of finite covers arXiv:1505.07754 (to appear in Bulletin of the London Mathematical Society)
- Non-reductive automorphism groups, the Loewy filtration and K-stability (joint with Giulio Codogni) arXiv:1501.03372 (to appear in Annales de l'Institut Fourier)
- Alpha invariants and coercivity of the Mabuchi functional on Fano
manifolds arXiv:1412.1426 (to appear in Annales de la Faculté des Sciences de Toulouse)
- Uniform stability of twisted constant scalar curvature Kähler metrics arXiv:1412.0648 (to appear in Int. Math. Res. Notices)
- Alpha invariants and K-stability for general polarisations of Fano varieties arXiv:1307.6527 (Int. Math. Res. Notices 2015 Vol 16 pp. 7162-7189)
I organised a conference in Cambridge: Postgraduate Conference in Complex Geometry.
Conferences I've been to or am going to:
- European Congress of Mathematics Berlin, July 18 - 22 2016
- Recent Advances in Complex Differential Geometry, Institut de Mathématiques de Toulouse, June 13 - 22 2016
- British Algebraic Geometry meeting, ICMS, Edinburgh, 13 - 15 April 2016
- Moduli spaces and singularities in algebraic and Riemannian geometry, Simons Center for Geometry and Physics, September 14 - October 11 2015
- Postgraduate Conference in Complex Geometry, University of Cambridge, September 9 - 11 2015
- Cones and Positivity, Loughborough University, August 4 - 7 2015
- Summer Research Institute on Algebraic Geometry, University of Utah, Salt Lake City, July 13 - 17 2015
- British Algebraic Geometry meeting, University of Warwick, 22 - 24 September, 2014
- Edge Days, University of Edinburgh, 5 - 7 July 2014
- Asymptotic Aspects of Complex and Algebraic Geometry, Universita di Milano Bicocca, 23 - 28 June 2014
- Edge Days, University of Edinburgh, 6 - 8 June 2014
- Irish Workshop on Kähler Geometry and Geometric Analysis, University College Cork, 12 - 14 May 2014
- Minicourses on Stability, University of Coimbra, 10 - 12 April 2014
- Traumatic Workshop, Imperial College, 3 - 4 April 2014
- William Rowan Hamilton Geometry and Topology Workshop, Trinity College, Dublin 27 - 31 August 2013
- Ricci curvature: limit spaces and Kahler geometry, ICMS, Edinburgh 1 - 5 July 2013
- Edge Days, University of Edinburgh, 7 - 9 June 2013
- Compactifying Moduli Spaces, CRM Barcelona 27 - 31 May 2013