报告人：Jonathan Augusto Trejos Olmos（南方科技大学）
时间：2026年7月21日10:00
地点：物质科研楼C1124
The embedded contact homology (ECH) is a kind of Floer homology proposed by Hutchings in the 2000’s. It turns out that ECH is a great tool for studying low dimensional symplectic and contact geometry. Of particular interest is the relationship between the embedded contact homology and a toric contact manifolds. The reason for this is that the embedded contact complex of a three-dimensional toric contact manifold, conjecturally, can be described by a combinatorial model. For instance, the embedded contact complex of the round 3-dimensional torus was completely described by Hutchings and Sullivan in 2007.
In this talk we briefly describe the combinatorial nature of the embedded contact complex of the boundary of a concave and a convex toric domain. We delineate how the combinatorial behavior follows from the toric symmetry and the careful translation of geometrical notions into combinatorial notions. In particular we describe how we can use some indirect methods to deduce the existence of certain J-holomorphic curves relevant to describing the embedded contact complex of the boundary. This is joint work with Cristofaro-Gardiner, Hutchings, Ramos, Weiler and Yao.
