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.