Algebraic geometry · Beijing
I am an algebraic geometer working on derived categories, birational geometry, and mathematical realizations of gauged linear sigma models.
I currently hold a joint postdoctoral position at Tsinghua University and Imperial College London. I have been based at Tsinghua in Beijing since April 2026, where I am mentored by Will Donovan.
Previously, I was a postdoctoral researcher at the University of Antwerp and the University of Bologna. I completed my PhD at the University of Stavanger, supervised by Michał Kapustka.
Derived equivalence
We relate non-birational Calabi–Yau threefolds of degrees 33 and 21 by a mathematical gauged linear sigma model and prove that they are derived equivalent. With Michał Kapustka and Prajwal Samal.
Categorical reconstruction
We prove that a smooth complex del Pezzo surface of degree at most four is determined by the enhanced right orthogonal to its structure sheaf. We also study the smaller Clifford component of a conic bundle and construct spinor modifications producing generally non-isomorphic del Pezzo surfaces. With Xun Lin and Shizhuo Zhang.
Categorical resolutions
We consider a one-nodal Gushel-Mukai variety and investigate a flop between its geometric resolution and a quadric fibration over the projective plane. Then, we address the derived-categorical implications of this construction. With Kacper Grzelakowski and Shizhuo Zhang.
I am also interested in agent-based AI systems for long-horizon mathematical research: tools that help organize, retrieve, test, and develop mathematical ideas without losing the structure of the argument.
Research
These are the areas I am working on at present.
Exceptional collections, semiorthogonal decompositions and mutations provide powerful tools to understand derived categories of coherent sheaves and categorical resolutions of singularities, and to investigate the geometric information that they carry. The derived category is a very rigid invariant for a Fano variety, but the choice of an appropriate subcategory can lead to the construction of more subtle birational invariants. This approach can be extended to singular varieties by constructing semiorthogonal decompositions of the categorical resolution of singularities.
While the derived category is known to be an invariant up to isomorphism for smooth Fano and general type varieties, its behavior as a birational invariant in broader settings (e.g. flops and related constructions) remains the subject of open conjectures. In particular, there is substantial evidence suggesting that certain birational transformations, known as K-equivalences, should induce equivalences at the level of derived categories.
In physics, gauged linear sigma models are supersymmetric gauge theories that exhibit multiple phases. Unlike the original abelian models, non-abelian GLSMs can have several “geometric” phases, each corresponding to the geometry of a smooth projective variety. Conjecturally, the physical relationship between these phases is reflected mathematically by Fourier–Mukai functors inducing equivalences, or embeddings, between the derived categories of the associated varieties.
The classification of simple K-equivalences, i.e. crepant birational maps between smooth projective varieties which admit a common resolution whose morphism to either side is a single blowup along a smooth center, is closely related to the classification of special Fano varieties called roofs. These are varieties of Picard rank two, whose extremal contractions are projective bundles, and such that there is a line bundle which restricts to O(1) on the fibers of both contractions. Although the roof condition is rather restrictive, the classification is still an open problem.
Events
Seminars and study groups I have helped organize.
Organized with Will Donovan at the Yau Mathematical Sciences Center, Tsinghua University.
Beijing · 2026
A collaborative study seminar on stability conditions, moduli spaces, and birational geometry.
Bologna · Chemnitz · Nancy · 2021