Research Interest

I am interested in low-dimensional topology. My research to date has focused on using the tools from various Floer homology and gauge theoretic invariants to study knot concordance, homology bordism group, exotic smooth structures on 4-manifolds, knotted surfaces in 4-manifolds, and diffeomorphism groups of 4-manifolds.

List of Papers

Heegaard Floer invariants

  1. Corks, involutions and Heegaard Floer homology (with Irving Dai and Matthew Hedden), Journal of the European Mathematical Society, 25(6) (2023), 2319-2389.
  2. Equivariant knots and knot Floer homology (with Irving Dai and Matthew Stoffregen) Journal of Topology, 16(3) (2023), 1167-1236.
  3. Knot Floer homology and surgery on equivariant knots to appear in the Journal of Topology.
  4. The (2,1)-cable of the figure-eight knot is not smoothly slice (with Irving Dai, Sungkyung Kang, JungHwan Park and Matthew Stoffregen) to appear in the Inventiones Mathematicae.
  5. Rank-expanding satellites, Whitehead doubles, and Heegaard Floer homology (with Irving Dai, Matthew Hedden, and Matthew Stoffregen) to appear in the Journal of Topology.
  6. Gompf's cork and Heegaard Floer homology (with Irving Dai, and Ian Zemke), International Mathematics Research Notices, 2024, 18, 12663-12682.
  7. A note on cables and the involutive concordance invariants (with Kristen Hendricks).

Gauge theoretic invariants

  1. From diffeomorphisms to exotic phenomena in small 4-manifolds (with Hokuto Konno, and Masaki Taniguchi).
  2. Exotic Dehn twists on 4-manifolds (with Hokuto Konno, and Masaki Taniguchi).
  3. Involutions and the Chern-Simons filtration in instanton Floer homology (with Antonio Alfieri, Irving Dai, and Masaki Taniguchi).
  4. On localizing groups of exotic diffeomorphisms of 4-manifolds (with Hokuto Konno).
  5. Exotically knotted closed surfaces from Donaldson's diagonalization for families (with Hokuto Konno, and Masaki Taniguchi).