• Home
• CV
• Research
• Teaching/Mentoring

Most of my research has focused on Floer theory and its applications to questions involving cobordism, concordance, and exotic phenomena. Links to my papers and preprints can be found below.

Preprints:

• Khovanov homology and equivariant surfaces
  with Maciej Borodzik, Abhishek Mallick, and Matthew Stoffregen.
  
• Z-disks in CP2
  with Anthony Conway and Maggie Miller.
  To appear in Compositio Mathematica.
  
• 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.
  




Publications:

• Gompf's cork and Heegaard Floer homology
  with Abhishek Mallick and Ian Zemke.
  International Mathematics Research Notices, (18) (2024), 12663—12682.
  
• Rank-expanding satellites, Whitehead doubles, and Heegaard Floer homology
  with Matthew Hedden, Abhishek Mallick, and Matthew Stoffregen.
  Journal of Topology, 17(4) (2024), e70008.
  
• The (2,1)-cable of the figure-eight knot is not smoothly slice
  with Sungkyung Kang, Abhishek Mallick, JungHwan Park, and Matthew Stoffregen.
  Inventiones Mathematicae, 238(2) (2024), 371—390.
  
• Equivariant knots and knot Floer homology
  ith Abhishek Mallick and Matthew Stoffregen.
  Journal of Topology, 16(3) (2023), 1167—1236.
  
• Homology concordance and knot Floer homology
  with Jennifer Hom, Matthew Stoffregen, and Linh Truong.
  Mathematische Annalen, 390(4) (2024), 6111—6186.
  
• 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.