University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Almost Kähler geometry
Which geometric properties of a Riemannian manifold force the integrability of compatible almost complex structures?
Find canonical metrics, for example extremal metrics or metrics with other special properties.
Quaternionic Hermitian geometry
Higher categorical structures in differential geometry
Represent structure on moduli spaces using gerbes
Differential and Deligne cohomology
Prizes, Awards, and Scholarships:
DFG research fellowship 2017-2018
Major / Recent Publications:
- Closed almost-Kähler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are Kähler (joint with Mehdi Lejmi), arXiv:1709.05210, 2017.
- Chern's contribution to the Hopf problem: An exposition based on Bryant's paper (joint with Aleksy Tralle), arXiv:1708.02904, 2017. To appear in Differential Geometry and its Applications.
- Integrability theorems and conformally constant Chern scalar curvature metrics in almost Hermitian geometry (joint with Mehdi Lejmi), arXiv:1703.01323, 2017.
- The Canonical 2-Gerbe of a Complex Manifold, arXiv:1601:04819, 2016. To appear in Theory and Applications of Categories.
- Extremal K-contact metrics (joint with Mehdi Lejmi), arXiv:1410.1370, Mathematische Zeitschrift, December 2015, Volume 281, Issue 3, pp 673-687.
- Refinements of the Chern-Dold Character: Cocycle Additions in Differential Cohomology, arXiv:1404:2027, Journal of Homotopy and Related Structures, pp 1-17, 2015.
- Products in Generalized Differential Cohomology, arXiv:1112.4173v2, Algebraic & Geometric Topology 15-1 (2015), 65--83.
- A Bicategory Approach to Differential Cohomology, arXiv:1211.6832, 2012.