CH, GW and the geography of tight convex hypersurfaces

Russell Avdek

While convex hypersurfaces are well understood in 3d contact topology, we are just starting to explore their basic properties in high dimensions. I will describe how to compute contact homologies (CH) of their neighborhoods, which can be used to infer tightness in any dimension. Then I’ll give a general construction of high-dimensional convex hypersurfaces in the style of Gompf’s fiber sum. For these convex hypersurfaces, relative Gromov-Witten can often compute CH in the style of Diogo-Lisi. We’ll work through some interesting examples.

https://www.ias.edu/video/ch-gw-and-geography-tight-convex-hypersurfaces