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Research

My research focuses on symplectic geometry, various Floer-theoretic invariants, including wrapped Fukaya categories, and their interactions with representation theory, low-dimensional topology, and string topology. 

Symplectic and low-dimensional topology

  1. Orbifold Hecke algebras and ghost bubble censorship for orbifolds
    in preparation, with K. Honda, Y. Tian, and T. Yuan 

  2. Morse theory of loop spaces and Hecke algebras 
    with K. Honda, Y. Tian, and T. Yuan, [arXiv, video, slides]

  3. Heegaard Floer Symplectic homology and Viterbo's isomorphism theorem in the context of multiple particles  with T. Yuan, [arXiv, video, slides]

  4. Combinatorial proof of Maslov index formula in Heegaard Floer Theory
    Algebraic & Geometric Topology (2024), [arXiv, video, slides]

Earlier research on toric topology

  1. Dolbeault cohomology of complex manifolds with torus action with T. Panov
    V. A. Rokhlin-Memorial. Topology, Geometry, and Dynamics V. A. Rokhlin-Memorial, Contemp. Math., 772 (2021). [arXiv, video]

  2. Basic Cohomology of Complex Moment-Angle Manifolds with H. Ishida and T. Panov
    International Mathematics Research Notices (2020) [arXiv]

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