Most of my research has focused on Floer theory and its applications. An annotated bibliography of selected works can be found here. A more in-depth description of my research and the questions that I am interested in can be found here (slightly outdated). Links to my papers and preprints can be found below.
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Rank-expanding satellites, Whitehead doubles, and Heegaard Floer homology
with Matthew Hedden, Abhishek Mallick, and Matthew Stoffregen.
Preprint.
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The (2,1)-cable of the figure-eight knot is not smoothly slice
with Sungkyung Kang, Abhishek Mallick, JungHwan Park, and Matthew Stoffregen.
Preprint.
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Equivariant knots and knot Floer homology
with Abhishek Mallick and Matthew Stoffregen.
Preprint.
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Homology concordance and knot Floer homology
with Jennifer Hom, Matthew Stoffregen, and Linh Truong.
Preprint.
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Instanton Floer homology of almost-rational plumbings
with Antonio Alfieri, John A. Baldwin, and Steven Sivek.
To appear in Geometry & Topology.
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Corks, involutions, and Heegaard Floer homology
with Matthew Hedden and Abhishek Mallick.
To appear in Journal of the European Mathematical Society.
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The 0-concordance monoid is infinitely generated
with Maggie Miller.
To appear in Proceedings of the American Mathematical Society.
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More concordance homomorphisms from knot Floer homology
with Jennifer Hom, Matthew Stoffregen, and Linh Truong.
Geometry & Topology, 25 (2021), 275—338.
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An infinite-rank summand of the homology cobordism group
with Jennifer Hom, Matthew Stoffregen, and Linh Truong.
To appear in Duke Mathematical Journal.
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Connected Heegaard Floer homology of sums of Seifert fibrations
Algebraic & Geometric Topology, 19 (2019), 2535—2574.
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On homology cobordism and local equivalence between plumbed manifolds
with Matthew Stoffregen.
Geometry & Topology, 23 (2019), 865—924.
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Involutive Heegaard Floer and plumbed three-manifolds
with Ciprian Manolescu.
Journal of the Institute of Mathematics of Jussieu, 18(6) (2019), 1115—1155.
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On the Pin(2)-equivariant monopole Floer homology of plumbed 3-manifolds
The Michigan Mathematical Journal, 67(2) (2018), 423—447.
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Diameter bounds and recursive properties of Full-Flag Johnson graphs
Discrete Mathematics, 341(7) (2018), 1932—1944.
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Combinatorial properties of Full-Flag Johnson graphs
Combinatorial Algorithms, IWOCA 2015, 112—123
Lecture Notes in Computer Science (9538), Springer (2016).
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On rationally ergodic and rationally weakly mixing rank-one transformations
with Xavier Garcia, Tudor Pădurariu, and Cesar Silva.
Ergodic Theory and Dynamical Systems, 35 (2014), 1141—1164.