Dulip Piyaratne

I am an Associate Professor in the Mathematics Department of Xiamen University Malaysia. Previously, I was a Postdoctoral Research Associate in the Department of Mathematics at the University of Arizona, USA, and a Project Researcher 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.

Research Interests

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

Research Profiles

Research Papers

Published in Journals

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), Vol. 2019, No. 747 (2019). 175-219 (45 pages) arXiv Journal

Stability Conditions Under the Fourier-Mukai Transforms on Abelian Threefolds.

Quarterly Journal of Mathematics, 70 (2019), No. 1, 225-288 (64 pages) arXiv Journal

Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions (with Georg Oberdieck and Yukinobu Toda).

Journal of Algebraic Geometry, 31 (2022), 13-73 (61 pages). arXiv Journal

Other Papers

Proceedings of Kinosaki Symposium on Algebraic Geometry (2015), 117-130 (14 pages) arXiv Proceedings

Stability conditions, Bogomolov-Gieseker type inequalities and Fano 3-folds. Submitted, 2017 (41 pages) arXiv
Generalized Bogomolov-Gieseker type inequalities on Fano 3-folds (Withdrawn and 7th paper above supersedes and incorporates many results from this paper) arXiv

Masters Dissertation (University of Liverpool): Topology of Isolated Singularities

Scientific Reports

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.