Associate Professor Tu Junwu from the Institute of Mathematical Sciences (IMS) has recently published two papers in Advances in Mathematics, one of the most prestigious mathematics journals in the world.
The theories of Gromov-Witten (GW) invariant，Fan-Jarvis-Ruan-Witten (FJRW) invariant and Bershadsky-Cecotti-Ooguri-Vafa (BCOV) invariant are intimately associated with contemporary quantum field theory. The studies of these theories have attracted some of the most influential mathematicians and physicists of the past three decades. The theories have prompted the development of Symplectic Topology, and have profoundly influenced several research fields including symplectic geometry, algebraic geometry and integrable systems.
Prof.Tu’s research is aimed at unifying the aforementioned various invariant theories in the realm of category theory, in which the Caldararu-Costello-Tu (CCT) categorial invariant, introduced by Tu and his collaborators, is the center. In both his two 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 helped set the stage for further studies, in particular, explicit calculations of CCT categorical invariant for Calabi-Yau hypersurfaces, thus laying the foundation for his research.
“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 Chen Xiuxiong, the founding director of IMS and world renowned mathematician. “He is certainly among the very best of his generation”. Prof. Tu joined ShanghaiTech in 2018 when IMS was first established. He has already produced an astonishing number of good works in different areas and across different disciplines over the past 3 years.
Links to the articles:
https://www.sciencedirect.com/science/article/abs/pii/S0001870821001833
https://www.sciencedirect.com/science/article/abs/pii/S0001870821001213