Ruadhaí Dervan

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.

Conferences I've been to or am going to:

Constant Scalar Curvature Metrics in Kähler and Sasaki Geometry, CIRM Marseille, January 15 - 19 2018
British Algebraic Geometry meeting, Cambridge, September 11 - 13 2017
Symplectic geometry - celebrating the work of Simon Donaldson, Cambridge, August 14 - 18 2017
Moduli of K-stable varieties, Rome, July 10 - 14 2017
Symposium in Geometry and Differential Equations, AMSS Beijing, July 3 - 7 2017
Current Developments and New Directions in Kähler Geometry, University of Notre Dame, June 26 - 30 2017
Positivity in Algebraic and Complex Geometry, ICMS Edinburgh, April 24 - 27 2017
Stability and moduli spaces, American Institute of Mathematics San Jose, January 9 - 13 2017
Algebraic Geometry: Old and New, University of Oxford, September 26 - 30 2016
Hitchin 70, University of Oxford, September 9 - 11 2016
European Congress of Mathematics, Berlin, July 18 - 22 2016
Recent Advances in Complex Differential Geometry, Institut de Mathématiques de Toulouse, June 13 - 22 2016
British Algebraic Geometry meeting, ICMS Edinburgh, 13 - 15 April 2016
Moduli spaces and singularities in algebraic and Riemannian geometry, Simons Center for Geometry and Physics, September 14 - October 11 2015
Postgraduate Conference in Complex Geometry, University of Cambridge, September 9 - 11 2015
Cones and Positivity, Loughborough University, August 4 - 7 2015
Summer Research Institute on Algebraic Geometry, University of Utah, July 13 - 17 2015
British Algebraic Geometry meeting, University of Warwick, 22 - 24 September 2014
Edge Days, University of Edinburgh, 5 - 7 July 2014
Asymptotic Aspects of Complex and Algebraic Geometry, Universita di Milano Bicocca, 23 - 28 June 2014
Edge Days, University of Edinburgh, 6 - 8 June 2014
Irish Workshop on Kähler Geometry and Geometric Analysis, University College Cork, 12 - 14 May 2014
Minicourses on Stability, University of Coimbra, 10 - 12 April 2014
Traumatic Workshop, Imperial College, 3 - 4 April 2014
William Rowan Hamilton Geometry and Topology Workshop, Trinity College Dublin, 27 - 31 August 2013
Ricci curvature: limit spaces and Kahler geometry, ICMS Edinburgh 1 - 5 July 2013
Edge Days, University of Edinburgh, 7 - 9 June 2013
Compactifying Moduli Spaces, CRM Barcelona, 27 - 31 May 2013