Research

1. Reconstruction of Fano manifolds from the orthogonal to an exceptional coherent sheaf, arXiv:2610.21904, submitted for publication

2. A note on geometry of Bridgeland moduli spaces of Gushel-Mukai threefolds, arXiv:2608.07853, submitted for publication

3. The Stability Manifolds of Kuznetsov components of Prime Fano Threefolds (joint with Changping Fan and Zhiyu Liu), arXiv: 2310.16950, submitted for publication.

4. A Birational Equivalence of Moduli Spaces on Gushel-Mukai Threefolds (most parts are finished as undergrad research, Advisor: Andrei Caldararu).     

#4 Will not be published. Preprint here. Chapter 4 about irreducibility of moduli spaces on GM 3-folds with primitive character is updated 8/2/2025, and will be a part of #2.

Here are some good-to-know facts that I obtained by LLM. I will not publish them nor carefully write them down, but I examined their proof and guarantee that they are sound.

1. As a consequence of #3, we can actually show the stability manifolds of cases settled in #3 are connected and contractible. More generally, assume the existence of a stability condition, then stability manifold of any fractional CY category with fraction d < 2 is just C \times H, whose AI generated proof is posted. (updated 10/22/2026, generated by ChatGPT Astra on 10/06/2026)

2. As a complement of Ziqi Liu's result, the Kuznetsov component of cubic threefolds is also indecomposable. Here is the reason.(updated 10/22/2026, generated by ChatGPT Astra on 09/27/2026)