Last Update 2022/11/21
I am mostly interested in developing and using categorical tools to investigate symplectic manifolds. Thesetools include (wrapped) Fukaya categories and microlocal sheaves. For that reason, I also work on higher structures, particularly the differential graded categories and A-infinity categories.
Currently, I am thinking of applications and improvements of our "homotopy colimit" formula with my collaborator Sangjin Lee, which allows us to practically compute wrapped Fukaya categories of Weinstein manifolds via first calculating them locally, then gluing them together by taking homotopy colimit. Computations for plumbing spaces and quiver varieties, deriving formulas for knot contact homology and Heegaard Floer homology, and locally studying homological mirror symmetry are some of the potential applications. In addition, I am interested in studying structures on (wrapped) Fukaya categories, such as stability conditions/entropy and cluster structures.
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