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Most of my research has focused on Floer theory and its applications to questions involving cobordism and/or concordance. A brief description of my research and the questions that I am interested in (written one or two years ago) can be found here. Links to my papers and preprints can be found below.

Preprints:

• Z-disks in CP2
  with Anthony Conway and Maggie Miller.
  
• Gompf's cork and Heegaard Floer homology
  with Abhishek Mallick and Ian Zemke.
  To appear in International Mathematics Research Notices.
  
• Involutions and the Chern-Simons filtration in instanton Floer homology
  with Antonio Alfieri, Abhishek Mallick, and Masaki Taniguchi.
  
• Lattice homology and Seiberg-Witten-Floer spectra
  with Hirofumi Sasahira and Matthew Stoffregen.
  
• Rank-expanding satellites, Whitehead doubles, and Heegaard Floer homology
  with Matthew Hedden, Abhishek Mallick, and Matthew Stoffregen.
  
• The (2,1)-cable of the figure-eight knot is not smoothly slice
  with Sungkyung Kang, Abhishek Mallick, JungHwan Park, and Matthew Stoffregen.
  To appear in Inventiones Mathematicae.
  
• Homology concordance and knot Floer homology
  with Jennifer Hom, Matthew Stoffregen, and Linh Truong.
  To appear in Mathematische Annalen.
  




Publications:

• Equivariant knots and knot Floer homology
  with Abhishek Mallick and Matthew Stoffregen.
  Journal of Topology, 16(3) (2023), 1167—1236.
  
• Instanton Floer homology of almost-rational plumbings
  with Antonio Alfieri, John A. Baldwin, and Steven Sivek.
  Geometry & Topology, 26(5) (2022), 2237—2294.
  
• Corks, involutions, and Heegaard Floer homology
  with Matthew Hedden and Abhishek Mallick.
  Journal of the European Mathematical Society, 25(6) (2023), 2319—2389.
  
• The 0-concordance monoid admits an infinite linearly independent set
  with Maggie Miller.
  Proceedings of the American Mathematical Society, 151(8) (2023), 3601—3609.
  
• More concordance homomorphisms from knot Floer homology
  with Jennifer Hom, Matthew Stoffregen, and Linh Truong.
  Geometry & Topology, 25(1) (2021), 275—338.
  
• An infinite-rank summand of the homology cobordism group
  with Jennifer Hom, Matthew Stoffregen, and Linh Truong.
  Duke Mathematical Journal, 172(12) (2023), 2356—2432.
  
• Connected Heegaard Floer homology of sums of Seifert fibrations
  Algebraic & Geometric Topology, 19 (2019), 2535—2574.
  
• On homology cobordism and local equivalence between plumbed manifolds
  with Matthew Stoffregen.
  Geometry & Topology, 23(2) (2019), 865—924.
  
• Involutive Heegaard Floer and plumbed three-manifolds
  with Ciprian Manolescu.
  Journal of the Institute of Mathematics of Jussieu, 18(6) (2019), 1115—1155.
  
• On the Pin(2)-equivariant monopole Floer homology of plumbed 3-manifolds
  The Michigan Mathematical Journal, 67(2) (2018), 423—447.
  
• Diameter bounds and recursive properties of Full-Flag Johnson graphs
  Discrete Mathematics, 341(7) (2018), 1932—1944.
  
• Combinatorial properties of Full-Flag Johnson graphs
  Combinatorial Algorithms, IWOCA 2015, 112—123
  Lecture Notes in Computer Science (9538), Springer (2016).
  
• 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.