Research

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) (rough!) lecture notes from Singularities and low-dimensional topology semester in Budapest.  

On Heegaard Floer homology:

• 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

• An involutive dual knot surgery formula (2022) with Kristen Hendricks, Jen Hom, and Ian Zemke

• 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

• Surgery Exact Triangles in Involutive Heegaard Floer homology (2020) with Kristen Hendricks, Jen Hom, and Ian Zemke

• 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

• 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

• 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:

• Localization in Khovanov homology (2018) with Melissa Zhang

• 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)