I am interested in the application of Floer theory to low-dimensional topology. I tend to think about equivariant and homotopy-theoretic aspects of Floer homology.
Expository:
A tour of monopole Floer Spectra (2023) lecture notes from Singularities and low-dimensional topology semester in Budapest.
On Heegaard Floer homology:
The link surgery formula and equivariant surgeries (2025) with Kristen Hendricks, Abhishek Mallick, and Ian Zemke
A note on the involutive invariant of splices (2024) with Kristen Hendricks and Ian Zemke (Algebraic and Geometric Topology)
PL-genus of surfaces in homology balls (2023) with Jen Hom and Hugo Zhou
Rank-expanding satellites, Whitehead doubles, and Heegaard Floer homology (2022) with Irving Dai, Matt Hedden, and Abhishek Mallick
The (2,1)-cable of the figure-eight knot is not smoothly slice (2022) with Irving Dai, Sungkyung Kang, Abhishek Mallick, and JungHwan Park (Inventiones Mathematicae)
An involutive dual knot surgery formula (2022) with Kristen Hendricks, Jen Hom, and Ian Zemke (Journal of Symplectic Geometry)
Naturality and functoriality in involutive Heegaard Floer homology (2022) with Kristen Hendricks, Jen Hom, and Ian Zemke
Equivariant knots and knot Floer homology (2022) with Irving Dai and Abhishek Mallick
Homology concordance and knot Floer homology (2021) with Irving Dai, Jen Hom, and Linh Truong
A note on PL-disks and rationally slice knots (2021) with Kristen Hendricks, Jen Hom, and Ian Zemke
On the quotient of the homology cobordism group by Seifert spaces (2021) with Kristen Hendricks, Jen Hom, and Ian Zemke
Linear Independence of Rationally Slice Knots (2020) with Jen Hom, Sungkyung Kang, and JungHwan Park (Geometry and Topology)
Surgery Exact Triangles in Involutive Heegaard Floer homology (2020) with Kristen Hendricks, Jen Hom, and Ian Zemke (Memoirs of the American Math Society)
More concordance homomorphisms from knot Floer homology (2019) with Irving Dai, Jen Hom, and Linh Truong (Geometry and Topology)
An infinite rank summand of the homology cobordism group (2018) with Irving Dai, Jen Hom, and Linh Truong (Duke Math Journal)
On homology cobordism and local equivalence between plumbed manifolds (2017) with Irving Dai (Geometry and Topology)
On Monopole Floer homology:
Lattice homology and Seiberg-Witten-Floer spectra (2023) with Irving Dai and Hirofumi Sasahira
Seiberg-Witten Floer spectra for b_1>0 (2021) with Hirofumi Sasahira (Memoirs of the European Math Society)
A remark on Pin(2)-equivariant Floer homology (2016) (Michigan Mathematics Journal)
Manolescu invariants of connected sums (2017) (Proceedings of the London Mathematical Society)
Pin(2)-equivariant Seiberg-Witten Floer homology of Seifert fibrations (2015) (Compositio Mathematica)
On Khovanov homology:
Khovanov homology and equivariant surfaces (2025) with Maciej Borodzik, Irving Dai, and Abhishek Mallick
Jones-Wenzl projectors and the Khovanov homotopy of the infinite twist. (2024) with Michael Willis (Quantum Topology)
Localization in Khovanov homology (2018) with Melissa Zhang (Geometry and Topology)
An odd Khovanov homotopy type (2018) with Sucharit Sarkar and Christopher Scaduto (Advances in Math)
On Instanton homology:
On Newstead's Mayer-Vietoris argument in characteristic 2 (2017) with Christopher Scaduto (International Journal of Mathematics)
The cohomology of rank two stable bundle moduli: mod two nilpotency & skew Schur polynomials (2017) with Christopher Scaduto (Canadian Journal of Mathematics)
Two-fold quasi-alternating links, Khovanov homology and instanton homology (2017) with Christopher Scaduto (Quantum Topology)
Klein-four connections and the Casson invariant for non-trivial admissible U(2) bundles (2017) with Christopher Scaduto (Algebraic and Geometric Topology)