I am an FNRS postdoctoral researcher at the Université Libre de Bruxelles working in gauge theory and complex geometry. Specifically, I study moduli spaces of Hermtian-Yang-Mills connections and different geometric flows on Kähler and projective manifolds. I am particularly interested in the phenomenon of singularity formation of different geometric objects in this setting. For moduli spaces this means understanding what happens at the boundary, and for flows it usually means understanding the asymptotics in a precise way. This often involves algebraic geometry, and several complex variables. In particular, my work employs different aspects of the theory of coherent sheaves in a fundamental and extensive fashion.
Here is a list of my publications:
- “Complex algebraic compacti cations of Hermitian-Yang-Mills moduli space” (with Daniel Greb, Matei Toma, and Richard Wentworth), arXiv:1810.00025, 95 pages. To appear in Geometry & Topology.
- “Continuity of the Yang-Mills flow on the set of semistable bundles” (with Richard Wentworth), to appear in Pure and Applied Mathematics Quarterly arxiv1904.02312 , 18 pages.
- “Analytic cycles, Bott-Chern forms, and singular sets for the Yang-Mills flow on Kähler manifolds” (with Richard Wentworth), Advances in Mathematics, 279 (2015), 501-531. See also arXiv:1402.3808.
- “Asymptotics of the Yang-Mills flow for holomorphic vector bundles over Kähler manifolds: the canonical structure of the limit”, Journal für die reine und angewandte Mathematik (Crelle’s Journal), Volume 2015, Issue 706, Pages 123-191. See also arXiv:1206.5491v4.
Work in progress
- “Long-time existence and singularity formation for the Calabi flow on a ruled surface” (joint with Joel Fine).
- “Glueing holomorphic bundles on Calabi-Yau threefolds” (working title, joint with Aleksander Doan and Yuuji Tanaka).
Here is a copy of my CV.