Edited Book
Recent Developments in Algebraic Geometry; to Miles Reid for his 70th birthday, London Mathematical Society Lecture Note Series (2022), Co-editors: Gavin Brown, Alexander Kasprzyk, Shigefumi Mori.
Preprints
One-dimensional components in the K-moduli of smooth Fano 3-folds, 30 pages, with Ivan Cheltsov, Elena Denisova, Erroxe Etxabarri-Alberdi, Dongchen Jiao, Anne-Sophie Kaloghiros, Jesus Martinez-Garcia, Theodoros Papazachariou; link to arXiv.
Published/Accepted
On K-moduli of quartic threefolds, Algebraic Geometry (to appear), 26 pages, with Ivan Cheltsov, Alexander Kasprzyk, Yuchen Liu, and Andrea Petracci; link to arXiv.
Double Veronese cones with 28 nodes, L'Enseignement Mathématique (to appear), 47 pages, with Ivan Cheltsov, Jihun Park, and Konstantin Shramov; link to arXiv.
Seshadri constants and K-stability of Fano manifolds, Duke Math Journal (2023) 172(6), 1109–1144, with Ziquan Zhuang; link to arXiv.
K-stability of Fano varieties via admissible flags, Forum of Mathematics Pi (2022), vol 10:e-15, 43 pages, with Ziquan Zhuang; link to journal (open access).
Stability of fibrations over one-dimensional bases, Duke Math Journal, (2022) 171(12), 2461–2518, with Maksym Fedorchuk and Igor Krylov; link to arXiv.
Birational rigidity of orbifold degree 2 del Pezzo fibrations, Nagoya Math Journal, 248 (2022), 888–921, with Igor Krylov; link to journal (open access).
On geometry of Fano threefold hypersurfaces, Rationality of Varieties, Progress in Math, 342 (2021), 1–14, with Ivan Cheltsov and Jihun Park. link to journal (open access).
Stable rationality of higher dimensional conic bundles, Épijournal Geom Algébrique, 2 (2018), Art. 5, 13 pages, with Okada Takuzo; link to journal (open access).
On a conjecture of Tian, Mathematische Zeitschrift, 288 (2018), no. 1-2, 217–241, with Ivan Cheltsov and Josef Schicho; link to journal (open access).
Birationally rigid pfaffian Fano 3-folds, Algebraic Geometry, (2018) Volume 5, Issue 2, 160–199, with Okada Takuzo; link to journal (open access).
Geometric aspects of robust testing for normality and sphericity, Stochastic Analysis and Applications, (2017) 35(3), 511–532, with Wolf-Dieter Richter, Lubos Strelec and Milan Stehlik.
On pliability of del Pezzo fibrations and Cox rings, J Reine Angew Math (Crelle’s Journal), 2017 (723), 101–125; link to arXiv.
On conjugacy classes of the Klein simple group in Cremona group, Glasgow Math Journal, 59 (2017), no. 2, 395–400; link to journal (open access).
Mori dream spaces and birational rigidity of Fano 3-folds, Advances in Mathematics, 292 (2016), 410–445, with Francesco Zucconi; link to journal (open access).
Non-rigid quartic 3-folds, Compositio Mathematica, volume 152 (2016), 955–983, with Anne-Sophie Kaloghiros; link to journal (open access).
Circle of Sarkisov links on a Fano 3-fold, Proc Edinburgh Math Soc, (2) 60 (2016), no. 1, 1–16, with Francesco Zucconi, link to arXiv.
An algebraic study of linkages with helical joints, J Pure Appl Algebra, 219 (2015), 2245–2259, with Zijia Li and Josef Schicho; link to arXiv.
Singular del Pezzo fibrations and birational rigidity, Automorphisms in Birational and Affine Geometry, Spring Proc Math Stat, 79 (2014), 3–15; link to journal (open access).
On del Pezzo fibrations that are not birationally rigid, J London Math Soc, (86) 2012, no. 1, 36–62; link to arxiv.
Grants supporting my research
Royal Society ISPF (PI), joint with Kento Fujita (Osaka, Japan), April 2024 – March 2027, £219,072
EPSRC Small Grant (PI), K-stable Fano 3-folds, Sept 2024 – Aug 2025, £37,142.
EPSRC New Horizons Grant (PI), Kähler-Einstein metrics on Fano manifolds, July 2021 – July 2024, £202,211
EPSRC New Investigator Award (PI), Birational Models of Singular Fano 3-folds, Oct 2020 – Sept 2022, £234,599
EPSRC-GCRF (Co-I): Capacity building in Africa via technology-driven research in algebraic and arithmetic geometry, Apr 2020 – Mar 2022, £170,892
GRAnD mini-CDT (PI), Oct 2017 – Mar 2021, [Centre for Doctoral Training to explore Geometry and its Applications] Approximately £350,000
Loughborough IAS Semester in Geometry, Sept 2018 – Jul 2019, £25,000
HIMR Focused Research Grant, Sept 2015 – Mar 2016, £10,000
Research in pairs, CIRM, Trento, Italy, with Ivan Cheltsov and Konstantin Shramov
Research in pairs, CIRM, Trento, Italy, with Francesco Zucconi
Activities Organised
VI BrAG meeting, University of Sheffield, 10-12 Apr 2024
Fano varieties, their geometry and moduli, Seoul, South Korea 30 Oct - 3 Nov 2023
Kodaira Workshop, Loughborough 15-16 Mar 2019
Workshop on Fano varieties and their automorphisms, Loughborough 30 Oct-2 Nov 2018
LMS Midlands Regional Meeting, Loughborough 18-21 Sept 2017
Edge Days, Edinburgh 26-30 Jun 2017
Spring Meeting in Algebraic Geometry, Tehran 8-13 Apr 2017
Workshop on Birational Geometry, Warwick 10-12 Feb 2016
Workshop on Rationality Questions, Bristol 6-8 Jan 2016
Travel Plans (since Jan 2023)
14-31 July 2025: Summer Research Institute in Algebraic Geometry, Colorado, USA
9-13 June 2025: Structures and Symmetries in Algebraic Geometry, Krakow, Poland.
2-6 June 2025: Real Algebraic Geometry and Birational Geometry, CIRM, France
24-28 March: Workshop on Birational Geometry, Pohang, South Korea
10-21 March 2025: Research in Residence, CIRM, France
3-7 March 2025: School on K-stability, CIRM, France
16-18 Dec 2025: Algebraic Geometry workshop, Sydney, Australia
9-13 Dec 2024: Algebraic Geometry in MATRIX, Creswick, Australia
18 Oct - 1 Nov 2024: Workshop on Birational Geometry and Number Theory, ICMS, Edinburgh, UK.
7-11 Oct 2024: Jürgen Hausen's 60th birthday conference, Innsbruck, Austria
9-13 Sept 2024: Conference in Algebraic Geometry, Cetraro, Italy
1-5 July 2024: BRIDGES conference on gauge theory, extremal structures, and stability, Corsica
20-31 May 2024: Research in Residence, CIRM, France
13-17 May 2024: K-stability and moment maps, Cambridge, UK
1 April - May 17 2024: Issac Newton Institute, Cambridge, UK
15-17 March 2024: AGNES, Boston, USA
30 Oct - 3 Nov 2023: Fano varieties, their geometry and moduli, Seoul, South Korea
25-29 Sept 2023: K-stability and Birational Geometry, Clay Institute, Oxford, UK
31 July - 4 August 2023: Modern Perspectives on Birational Geometry, Taipei, Taiwan
8-12 May 2023: Higher Dimensional Geometry, Simons Center, New York, USA
26 Feb - 3 March 2023: Explicit Moduli Problems in Higher Dimensions, Banff, Canada
23-27 Jan 2023: Winter School on K-stability of Fano Varieties, Trento, Italy