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.

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

I am currently teaching the SMSTC course Riemann Surfaces.

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

I am advertising **two PhD positions** to work with me, to begin in September 2024, funded by my Royal Society University Research Fellowship. If you might be interested in these positions and doing a PhD in algebraic or differential geometry, please contact me by email. The current deadline to apply is December 15th, but please contact me before then. I especially welcome applications from those from underrepresented groups. 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:**

- On divisorial stability of finite covers
*(with Theo Papazachariou)*arXiv:2306.07141 (abstract) - 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
*(to appear in Forum Math. Sigma)*(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*(Math. Ann. 385 (2023) pp. 357-291)*(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)

**Postdocs:**

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

**PhD students:**

- Mahmoud Elimam, PhD student at SISSA Trieste, co-supervised by Jacopo Stoppa (2023 - present)
- Gabriel Frey, PhD student at the University of Glasgow (2023 - present)
- Annamaria Ortu, PhD student at SISSA Trieste, co-supervised by Jacopo Stoppa (2020 - 2023)
- 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)

**Master's students and undergraduate research students:**

- Alexia Corradini, visiting M1 master's student from École Polytechnique (spring/summer 2022)
- Ioannis Karagiorgis, undergraduate research, co-supervised by Theo Papazachariou (summer 2023)
- Theresa Ortscheidt, undergraduate research, co-supervised by Theo Papazachariou (summer 2023)
- Ho Leung Fong, undergraduate summer research student (summer 2021)
- Qiangru Kuang, undergraduate summer research student (summer 2019)

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. As part of this, I am organising the workshop K-stability and moment maps held there from May 13th to 17th 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.