I'm a Senior Lecturer and Royal Society University Research Fellow at the University of Glasgow (I hope to move my website there very soon...). I've previously spent parts of my career and education at the University of Cambridge (where I was a fellow of Gonville & Caius College), École Polytechnique, Université libre de Bruxelles and Trinity College Dublin.

My first name is pronounced "Rui" (the "dh" is silent, it's Irish).

I research complex geometry, which is roughly the intersection of algebraic and differential geometry. At the moment most of my work lies between the two sides; in the past I've also worked on purely algebraic and purely analytic problems. Much of my research is motivated by linking geometric partial differential equations (determining "canonical metrics") to notions of stability in algebraic geometry. The most famous example of this sort of correspondence is what is known as the Yau-Tian-Donaldson conjecture, which links K-stability to the existence of constant scalar curvature Kähler metrics (a prominent special case of these metrics being Kähler-Einstein metrics). I'm also interested in a wide range of algebraic and analytic topics that enter into this field, such as moduli theory, geometric invariant theory, geometric analysis, birational geometry, non-Archimedean geometry, Bridgeland stability conditions, positivity properties in complex geometry (à la Demailly), pluripotential theory...

Donaldson has written a compelling survey of my area, Székelyhidi's book (see also similar notes) and Thomas' notes are excellent introductions.

My CV. My email address is ruadhai.dervan@glasgow.ac.uk.

I would be very happy to take more PhD students, and if you are interested please contact me. My current and previous students have worked on a range of topics in complex differential and algebraic geometry, they all used a lot of both (complex) differential and algebraic geometry (there is no need to start already knowing complex geometry, however). Similarly please contact me if you might like to do a postdoc in Glasgow (and you work on topics related to my research interests described above), and I can explain various funding sources.

Papers and preprints:

- Ding stability and Kähler-Einstein metrics on manifolds with big anticanonical class
*(with Rémi Reboulet)*arXiv:2209.08952 (abstract) - Stability conditions in geometric invariant theory arXiv:2207.04766 (abstract)
- Extremal Kähler metrics on blowups
*(with Lars Sektnan)*arXiv:2110.13579 (abstract) - Stability conditions for polarised varieties arXiv:2103.03177 (video) (abstract)
*Z*-critical connections and Bridgeland stability conditions*(with John McCarthy and Lars Sektnan)*arXiv:2012.10426 (video) (abstract)- Valuative stability of polarised varieties
*(with Eveline Legendre)*arXiv:2010.04023*(to appear in Math. Ann.)*(abstract) - Uniqueness of optimal symplectic connections
*(with Lars Sektnan)*arXiv:2003.13626*(Forum Math. Sigma. Vol 9 (2021) e18, pp. 1-37)*(video) (abstract) - Moduli theory, stability of fibrations and optimal symplectic connections
*(with Lars Sektnan)*arXiv:1911.12701*(Geom. Topol. 25-5 (2021), pp. 2643-2697)*(video) (abstract) - Optimal symplectic connections on holomorphic submersions
*(with Lars Sektnan)*arXiv:1907.11014*(Comm. Pure Appl. Math. Vol. 74 no. 10 (2021), pp. 2134-2184)*(abstract) - K-semistability of optimal degenerations arXiv:1905.11334
*(Q. J. Math. Vol. 71 (2020) Issue 3, pp. 989-995)*(abstract) - Moduli of polarised manifolds via canonical Kähler metrics
*(with Philipp Naumann)*arXiv:1810.02576 (video) (abstract) - Extremal metrics on fibrations
*(with Lars Sektnan)*arXiv:1712.05374*(Proc. Lond. Math. Soc. (3) 120 (2020) pp. 587-616)*(video) (abstract) - Stable maps in higher dimensions
*(with Julius Ross)*arXiv:1708.09750*(Math. Ann. Vol. 374 (2019) no. 3-4, pp. 1033-1073)*(abstract) - Hermitian Yang-Mills connections on blowups
*(with Lars Sektnan)*arXiv:1707.07638*(J. Geom. Anal. Vol. 31 (2021), pp. 516-542)*(abstract) - The Kähler-Ricci flow and optimal degenerations
*(with Gábor Székelyhidi)*arXiv:1612.07299*(J. Differential Geom. Vol. 116 (2020), no. 1 pp. 187-203)*(abstract) - Relative K-stability for Kähler manifolds arXiv:1611.00569
*(Math. Ann. Vol. 372 (2018), no. 3-4, pp. 859-889)*(addendum) (abstract) - K-stability for Kähler manifolds
*(with Julius Ross)*arXiv:1602.08983*(Math. Res. Lett. Vol. 24, No. 3 (2017), pp. 689-739)*(abstract) - A finite dimensional approach to Donaldson's J-flow
*(with Julien Keller)*arXiv:1507.03461*(Comm. Anal. Geom. (2019) Vol. 27, no. 5. pp. 1025-1085)*(abstract) - On K-stability of finite covers arXiv:1505.07754
*(Bull. London Math. Soc. (2016) 48 (4) pp. 717-728)*(abstract) - 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) (abstract) - 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)*(abstract) - Uniform stability of twisted constant scalar curvature Kähler metrics arXiv:1412.0648
*(Int. Math. Res. Notices (2016) Vol 15 pp. 4728-4783)*(abstract) - Alpha invariants and K-stability for general polarisations of Fano varieties arXiv:1307.6527
*(Int. Math. Res. Notices (2015) Vol 16 pp. 7162-7189)*(abstract)

- Annamaria Ortu, PhD student at SISSA Trieste, co-supervised by Jacopo Stoppa (2020 - present)
- John McCarthy, PhD student at Imperial College, co-supervised by Simon Donaldson (2019 - 2022)
- Michael Hallam, DPhil student at the University of Oxford, co-supervised by Frances Kirwan (2018 - 2022)
- Alexia Corradini, visiting M1 master's student from École Polytechnique (spring/summer 2022)
- Ho Leung Fong, undergraduate summer research student (summer 2021)
- Qiangru Kuang, undergraduate summer research student (summer 2019)

Postdocs:

- Theo Papazachariou (2022 - present)
- Rémi Reboulet (2022)

Photos with Michael, John and Annamaria (Aarhus, June 2022) and Alexia and Rémi (Cambridge, August 2022).

I am organising a six-month programme titled New equivariant methods in algebraic and differential geometry along with several others at the Isaac Newton Institute in 2024. I've previously conferences and workshops in Cambridge (Cambridge complex geometry afternoon, 2022), Cambridge (K-stability and Kähler geometry, 2021), Newcastle (Newcastle complex geometry workshop, 2018), Rome (Moduli of K-stable varieties, 2017) and Cambridge (Postgraduate conference in complex geometry, 2015). The Rome conference has an associated conference proceedings, also edited by Codogni and Viviani.

I taught Part III Complex Manifolds in Cambridge in Lent Term 2020 and Lent Term 2019. I am not teaching at the moment.