Professor Junwu Tu of the Institute of Mathematical Sciences has recently had two papers published in consecutive issues of Advances in Mathematics, one of the most prestigious mathematics journals in the world.
The theories of GW （Gromov-Witten）invariant，FJRW （Fan-Jarvis-Ruan-Witten）invariant and BCOV（Bershadsky-Cecotti-Ooguri-Vafa） invariant are intimately associated with the contemporary quantum field theory. Their studies have attracted some of the most influential mathematicians and physicists in the last three decades. The theories have spawned the development of Symplectic Topology, and have profoundly transformed the landscapes of other fields, including symplectic geometry, algebraic geometry and integrable systems.
Prof.Tu’s program has been to unify aforementioned various invariant theories in the realm of category theory. The CCT (Caldararu-Costello-Tu) categorial invariant, introduced by Tu together with his collaborators, is central to this program. In the pair of articles, Tu presented an explicit categorical construction of Calabi-Yau algebraic structure of a hypersurface and the splitting of the non-commutative Hodge filtration. These remarkable achievements have helped set the stage for further studies, and in particular, explicit calculations, of CCT categorical invariant for Calabi-Yau hypersurfaces and thus laid the foundation for his program.
“Junwu’s new series of highly original and non-trivial results has not only lent further credence to his ambitious program, but also solidified his establishment in the field”, said Professor Xiuxiong Chen, the founding director of IMS and world renowned mathematician. “He is certainly among the very best of his generation”.
Prof. Tu joint ShanghaiTech in 2018 when the institute first commenced. He has since produced an astonishing number of good works in different areas and across different disciplines.
Links to the articles:
https://www.sciencedirect.com/science/article/abs/pii/S0001870821001833
https://www.sciencedirect.com/science/article/abs/pii/S0001870821001213