Developed a real sutured Heegaard Floer theory.
problem Real sutured manifolds and their Floer homology.
method Real nice diagrams, combinatorial computation.
result New structural properties distinguishing from sutured Floer homology.
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Surgery obstructions extended to integer homology spheres using Heegaard Floer homology.
problem Obstructing knots in integer homology spheres using surgery.
method Extending Heegaard Floer homology obstructions to all integer homology spheres for both positive and negative surgeries.
result Deduced a lower bound on for smooth cobordism between integer homology spheres.
The paper tackles deeply slice knots via immersed curves.
problem Whether there exists a homology 3-sphere with certain knot properties.
method Constructing knots in contractible 4-manifolds and using Heegaard Floer homology invariants.
result Proves the existence of a class of deeply slice knots.
Classifies -space surgeries on all two-bridge links
problem Classifying -space surgeries on two-bridge links
method Introduces a sufficient diagrammatic condition for links in to be persistently foliar, defines a simplified model for Heegaard Floer homology, and uses Turaev torsions for computations
result Determines -space surgeries in the case of generalised -space links