# Rational homology disks and symplectic topology

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Andras Stipsicz, Renyi Institute, Hungary
Fine Hall 314

Surface singularities admitting a smoothing with the homology of the 4-disk (a so-called rational homology disk, QHD) play central role in the construction of exotic 4-manifolds through the "rational blow down process." Applying various forms of gauge theory we derive obstructions for a singularity to admit such smoothings. Using symplectic topology we classify all starshaped resolution graphs with QHD smoothings.