Abstract: From a surgical perspective, every contact manifold can be obtained from applying both isotropic and coisotropic surgeries on the standard contact sphere. Vanishing of contact homology, i.e. the incarnation of overtwistedness in symplectic field theory, can only arise from coisotropic surgeries, in particular, contact +1 surgeries. In this talk, I will explain situations of contact +1 surgeries yielding vanishing of contact homology both in dimension 3 and higher dimensions. In particular, I will explain contact +1 surgeries along any torus knots with maximal Thurston-Bennequin number produce tight contact manifolds with vanishing contact homology. This is partially joint with Youlin Li.
Bio: Zhengyi Zhou received his PhD degree form UC Berkeley in 2018. After that, he spent three years at IAS princeton as a postdoc. Starting from 2021, he is an associate professor at the Morningside Center of Mathematics, Academy of Mathematics and Systems Science. His research interest lies in symplectic and contact topology.
