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 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.

Papers and preprints:

- 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)* - 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 and 2016-2017.