I'm a Research Fellow at Gonville & Caius College, Cambridge. I'm spending the academic year 2017-2018 in Paris at École Polytechnique.
Previously I was a PhD student at the University of Cambridge, a visiting PhD student at the Université libre de Bruxelles and an undergaduate at Trinity College Dublin.
My first name is pronounced "Rui" (the "dh" is silent, it's Irish).
My research focuses on 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 theory 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.
Papers and preprints:
- Extremal metrics on fibrations (with Lars Sektnan) arXiv:1712.05374
- Stable maps in higher dimensions (with Julius Ross) arXiv:1708.09750
- 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 (to appear in Math. Annalen) Addendum.
- I wrote an appendix to Sjöström Dyrefelt's "On K-polystability of cscK manifolds with transcendental cohomology class", which removes a technical assumption from the main result of this paper, see arXiv:1711.11482. In particular the existence of an extremal metric on a Kähler manifold implies relative K-stability, without any assumptions on the norms of the objects involved.
- K-stability for Kähler manifolds (with Julius Ross) arXiv:1602.08983 (Math. Res. Lett. Vol. 24, No. 3 (2017), pp. 689-739)
- 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.
I ran the Cambridge Junior Geometry Seminar (called "Geometry Tea") in 2013-2014. It continued in 2014-2015, 2015-2016, 2016-2017 and 2018-2019.
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