My research involves the study Low Dimensional Topology: smooth four dimensional manifolds, three dimensional manifolds, and embedded circles (knots) inside three-manifolds. There are various mathematical methods used in this research: gauge theory, symplectic geometry, Floer homology and ideas from topological quantum field theory. Some of my more recent work on studying knots and surgery problems inside three-manifolds uses Heegaard Floer homology that was developed jointly with Peter Ozsvath.

Awards and Achievements

  • Veblen Prize ( 2007)