My mathematical endeavor in training and research so far mostly concerns algebraic and geometric questions motivated by homological mirror symmetry.
Some of my work:
J. Huang, G. Kerr and P. Zhou. Homological mirror symmetry for degenerate circuit transitions, work in progress.
J. Huang. GIT schobers, symplectic windows and mirror symmetry, work in progress.
A more concrete description for those interested in knowing more:
Roughly speaking, I have studied some semiorthogonal decompositions of Fukaya categories of some particular Landau-Ginzburg models that are, in principle, mirrors of the effect of some particular unbalanced variations of GIT quotients. A more algebraic direction along these lines involves studying properties of perverse schobers, which will play an import role in organizing these categories on both sides.
I am currently building what should be called the symplectic window category, whose counterpart under HMS is exactly the grade restriction rule, or the GIT window category. My approach should eventually work for ANY reductive group action on a quasi-projective variety.
Feel free to request for results I have so far.