Dr. Ruxuan Zhang, jointly with Davesh Maulik, Junliang Shen and Qizheng Yin, has online published a research paper by Inventiones Mathematicae. This is the 12th research paper authored by researchers in Shanghai Center for Mathematical Sciences that has published in one of the top-four international mathematical journals.

The paper is “The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles” (https://link.springer.com/article/10.1007/s00222-025-01339-8).

Derived categories serve as an important invariant for algebraic varieties. Kawamata, Bondal, and Orlov proposed the D-equivalence conjecture: the derived categories of two birationally equivalent Calabi-Yau varieties should be derived equivalent. The D-equivalence conjecture has been proven by Bridgeland for Calabi–Yau threefolds. However, very few cases of this conjecture are known in dimension > 4. Using equivalences obtained from window conditions, Halpern-Leistner proved the D-equivalence conjecture for any hyper-Kähler variety which can be realized as a Bridgeland moduli space of stable objects on a (possibly twisted) K3 surface.

Davesh Maulik, Junliang Shen, Qizheng Yin, and Ruxuan Zhang generalize Halpern- Leistner’s result, but the construction of the derived equivalences is very different. They obtain explicit Fourier–Mukai kernels which rely on the theory of moduli spaces of hyper-Kähler manifolds and hyperholomorphic bundles via Markman’s idea. Their method in fact proves the following stronger, twisted version of the D- equivalence conjecture involving arbitrary Brauer classes.

Dr. Zhang Ruxuan earned his Bachelor's degree from Nanjing University of Aeronautics and Astronautics, where he studied from 2012 to 2016. He received his Ph.D. from Fudan University in 2022. Following this, he conducted postdoctoral research at Peking University from 2022 to 2024, after which he returned to the Shanghai Mathematics Center to undertake a new postdoctoral position.