I work broadly in algebraic geometry with applications to mirror symmetry. I am particularly interested in log Gromov-Witten theory, moduli spaces, tropical geometry, real enumerative algebraic geometry, cluster varieties and Donaldson-Thomas theory of quiver representations.
My research is partially supported by the NSF grant DMS 2302116 New Bridges to Gromov-Witten theory.
PREPRINTS
The KSBA moduli space of stable log Calabi-Yau surfaces, joint with V. Alexeev, H. Argüz, P. Bousseau arXiv:2402.15117, 91 pages, submitted, Arxiv Link Video 1 Video 2
Quivers, Flow Trees, and Log Curves, joint with Pierrick Bousseau, Arxiv Link Video
PAPERS (published or in press at peer reviewed journals)
Quivers and curves in higher dimension, joint with Pierrick Bousseau, to appear at the Transactions of the American Mathematical Society, 2024. Arxiv Link Video
Fock-Goncharov dual cluster varieties and Gross-Siebert mirrors, joint with Pierrick Bousseau, published at the Journal für die reine und angewandte Mathematik (Crelles Journal), 2023. Arxiv Link Video
Equations of mirrors to log Calabi--Yau pairs via the heart of canonical wall structures, Mathematical Proceedings of the Cambridge Philosophical Society, 2023 Arxiv Link Video
Gromov--Witten invariants of complete intersections, joint with Pierrick Bousseau, Rahul Pandharipande and Dimitri Zvonkine, Journal of Topology, 2023 Arxiv Link Video
The flow tree formula for Donaldson-Thomas invariants of quivers with potentials, joint with Pierrick Bousseau, 50 pages, arXiv:2102.11200, Compositio Mathematica, 2022 Arxiv Link Video
The higher dimensional tropical vertex, joint with Mark Gross, Geometry & Topology, 2022 Arxiv Link Video 1 Video 2
Real log curves in toric varieties, tropical curves, and log Welschinger invariants, joint with Pierrick Bousseau, Annales de l’institut Fourier, 2022 Arxiv Link Slides
On the cohomology groups of real Lagrangians in Calabi-Yau threefolds, joint with Thomas Prince, 32 pages, arXiv:2002.03957, Experimental Mathematics, 2021 Arxiv Link
Real Lagrangians in Calabi-Yau Threefolds, joint with Thomas Prince, Proceedings of the London Mathematical Society, 2020 Arxiv Link
A note on Schoen’s Calabi–Yau Threefolds, joint with Thomas Prince, Rendiconti del Seminario Matematico, 2021 Arxiv Link
Mirror symmetry for the Tate curve via tropical and log corals, Journal of the London Mathematical Society, 2022 Arxiv Link Video
Real loci in (log-) Calabi-Yau manifolds via Kato-Nakayama spaces of toric degenerations, European Journal of Mathematics, 2021 Arxiv Link
Self dual metrics on non-simply connected 4-manifolds, joint with Mustafa Kalafat and Yildiray Ozan, Journal of Geometry and Physics, 2013 Arxiv Link
Complex and symplectic structures on Panelled Web 4-manifolds, joint with Mustafa Kalafat, Topology and its Applications, 2012 Arxiv Link
Peer-reviewed Conference Proceedings, Reports, Thesis:
Quiver DT Invariants and Log Gromov--Witten Theory of Toric Varieties, String-Math 2022 Proceedings, AMS Proceedings of Symposia in Pure Mathematics, 2024 Arxiv Link
The Quantum Mirror to the Quartic del Pezzo Surface, Lie theory and its applications in physics, Springer Proceedings in Mathematics and Statistics, 2023 Arxiv Link
Topological torus fibrations on Calabi--Yau manifolds via Kato--Nakayama spaces, Proceedings of GGT, Gokova Geometry Topology Conferences, 2021 Arxiv Link
Toric degenerations and tropical enumeration of real curves with Welschinger signs, Oberwolfach reports, 2019
Log-geometric techniques for open invariants in mirror symmetry. PhD thesis, University of Hamburg, available online here.
Floer theory for the Tate curve via tropical geometry, Oberwolfach reports 2015.
Real Lagrangians in Kato--Nakayama spaces, MSc thesis, University of Hamburg, 2013, available at departmental library of Universität Hamburg.