I am a Postdoctoral Research Associate in the Department of Mathematics at the University of Arizona, USA. Previously, I was a Project Researcher (= Postdoctoral Research Fellow) in Mathematics at the Kavli Institute for the Physics and Mathematics of the Universe, the University of Tokyo, Japan. I completed my PhD in 2014 at the University of Edinburgh, UK under Antony Maciocia.
- Algebraic Geometry: Derived categories, Stability conditions, Fourier-Mukai theory, Abelian varieties, Calabi-Yau manifolds, Moduli spaces of sheaves, Donaldson-Thomas theory, Mirror symmetry, Birational geometry
- Fourier-Mukai transforms and Bridgeland stability conditions on abelian threefolds (with Antony Maciocia). Algebraic Geometry (Foundation Compositio Mathematica) 2 (2015), no. 3, 270-297 (28 pages) arXiv Journal
- Fourier-Mukai transforms and Bridgeland stability conditions on abelian threefolds II (with Antony Maciocia). International Journal of Mathematics 27, 1 (2016), 1650007 (27 pages) arXiv Journal
- Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants (with Yukinobu Toda). J. Reine Angew. Math. (Crelle’s Journal), Available online and ahead of print, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, 2016 (45 pages) arXiv Journal
- Fourier-Mukai Transforms and Stability Conditions on Abelian Varieties. Proceedings of Kinosaki Symposium on Algebraic Geometry (2015), 117-130 (14 pages) arXiv Proceedings
- Stability Conditions Under the Fourier-Mukai Transforms on Abelian Threefolds. Quarterly Journal of Mathematics, Available online and ahead of print (64 pages) arXiv Journal
- Stability conditions, Bogomolov-Gieseker type inequalities and Fano 3-folds. Submitted, 2017 (41 pages) arXiv
- Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions (with Georg Oberdieck and Yukinobu Toda). Submitted, 2018 (58 pages) arXiv
- Generalized Bogomolov-Gieseker type inequalities on Fano 3-folds (Withdrawn and 6th paper above supersedes and incorporates many results from this paper) arXiv
PhD Thesis (University of Edinburgh): Fourier-Mukai transforms and stability conditions on abelian threefolds
Masters Dissertation (University of Liverpool): Topology of Isolated Singularities
- Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants, Research highlight, Kavli IPMU Annual Report (Apr. 2014 - Mar. 2015), 2016.
- Matrix factorization and related topics, Workshop report, Kavli IPMU News, Vol. 35, Sept. 2016.
A poster about my research contributions: Derived Categories and Stability Conditions
My talk at the Simons Centre (USA): Stability conditions and Fourier-Mukai theory
My talk at the Kavli IPMU (Japan): Modification of Bogomolov-Gieseker type inequality conjecture and Fano 3-folds