I'm a Senior Lecturer and Royal Society University Research Fellow at the University of Glasgow. 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. I'm interested in both the analytic and algebro-geometric sides of complex geometry, and at the moment most of my work lies somewhere between the two. Topics I'm currently interested in include Kähler geometry, K-stability, moduli theory, non-Archimedean geometry and geometric analysis, amongst others.

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

My CV. My email address is ruadhai.dervan@glasgow.ac.uk. My office is 439, University of Glasgow Mathematics & Statistics Building.

I am always happy to hear from prospective PhD students, and if you are interested in working with me please contact me (before December of the given year ideally). My current and previous students have worked on a range of topics in complex differential and algebraic geometry. Similarly please contact me if you might like to do a postdoc in Glasgow, and I can explain various funding sources.

Papers and preprints:

- The universal structure of moment maps in complex geometry
*(with Michael Hallam)*arXiv:2304.01149 (abstract) - The birational geometry of GIT quotients
*(with Rémi Reboulet)*arXiv:2301.09227 (abstract) - 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 Chicago (Around complex geometry), 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.