I'm a Research Fellow at Gonville & Caius College, Cambridge.
Previously I was a PhD student at the University of Cambridge, a visiting PhD student at the Université libre de Bruxelles and an undergaduate of Trinity College Dublin. I will spend the academic year 2017-2018 at École Polytechnique.
My first name is pronounced "Rui" (the "dh" is silent, it's Irish).
My research is in complex geometry and algebraic geometry. I am particularly interested in the existence of canonical metrics in complex geometry (e.g. Kähler-Einstein, extremal), notions of algebro-geometric stability (e.g. K-stability), and more generally moduli spaces and geometric analysis. My work is mostly motivated by the "Yau-Tian-Donaldson" conjecture, which links stability notions to the existence of canonical metrics.
My CV. My email address is rd430(at)cam.ac.uk.
Geometry Tea 2013-2014, 2014-2015, 2015-2016 and 2016-2017.
Papers and preprints:
- Hermitian Yang-Mills connections on blowups (with Lars Sektnan) arXiv:1707.07638
- The Kähler-Ricci flow and optimal degenerations (with Gábor Székelyhidi) arXiv:1612.07299
- Relative K-stability for Kähler manifolds arXiv:1611.00569
- K-stability for Kähler manifolds (with Julius Ross) arXiv:1602.08983 (to appear in Math. Res. Lett.)
- A finite dimensional approach to Donaldson's J-flow (with Julien Keller) arXiv:1507.03461 (to appear in Comm. Anal. Geom.)
- On K-stability of finite covers arXiv:1505.07754 (Bull. London Math. Soc. (2016) 48 (4) pp. 717-728.)
- Non-reductive automorphism groups, the Loewy filtration and K-stability (with Giulio Codogni) arXiv:1501.03372 (Annales de l'institut Fourier 66 no. 5 (2016) pp. 1895-1921.)
- Alpha invariants and coercivity of the Mabuchi functional on Fano
manifolds arXiv:1412.1426 (Ann. Fac. Sci. Toulouse Sér. 6, 25 no. 4 (2016), p. 919-934 )
- Uniform stability of twisted constant scalar curvature Kähler metrics arXiv:1412.0648 (Int. Math. Res. Notices (2016) Vol 15 pp. 4728-4783.)
- 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 Rome in 2017: Moduli of K-stable varieties.
I also organised a conference in Cambridge in 2015: Postgraduate Conference in Complex Geometry.
Conferences I've been to or am going to:
- Constant Scalar Curvature Metrics in Kähler and Sasaki Geometry, CIRM Marseille, January 15 - 19 2018
- British Algebraic Geometry meeting, Cambridge, September 11 - 13 2017
- Symplectic geometry - celebrating the work of Simon Donaldson, Cambridge, August 14 - 18 2017
- Moduli of K-stable varieties, Rome, July 10 - 14 2017
- Symposium in Geometry and Differential Equations, AMSS Beijing, July 3 - 7 2017
- Current Developments and New Directions in Kähler Geometry, University of Notre Dame, June 26 - 30 2017
- Positivity in Algebraic and Complex Geometry, ICMS Edinburgh, April 24 - 27 2017
- Stability and moduli spaces, American Institute of Mathematics San Jose, January 9 - 13 2017
- Algebraic Geometry: Old and New, University of Oxford, September 26 - 30 2016
- Hitchin 70, University of Oxford, September 9 - 11 2016
- 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, 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