I'm a Research Fellow at Gonville & Caius College, University of Cambridge. I've previously spent time in École Polytechnique, Université libre de Bruxelles and 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:

- Moduli of polarised manifolds via canonical Kähler metrics
*(with Philipp Naumann)*arXiv:1810.02576 - Extremal metrics on fibrations
*(with Lars Sektnan)*arXiv:1712.05374 - Stable maps in higher dimensions
*(with Julius Ross)*arXiv:1708.09750*(to appear in Math. Annalen)* - 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*(to appear in J. Differential Geom.)* - Relative K-stability for Kähler manifolds arXiv:1611.00569
*(to appear in Math. Annalen)*Addendum. - 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)*Corrigendum. - 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 conferences in Cambridge (Postgraduate Conference in Complex Geometry, 2015), Rome (Moduli of K-stable varieties, 2017) and Newcastle (Newcastle Complex Geometry Workshop, 2018).

I ran the Cambridge Junior Geometry Seminar (called "Geometry Tea") in 2013-2014. It continues in 2018-2019.