Geometry research

Areas of research interest include:

  • complex and Kähler geometry, canonical Kähler metrics
  • algebraic geometry, classification theory, Mori theory, Fano varieties
  • symplectic geometry
  • gauge-theory, knot theory, 3- and 4- dimensional topology
  • Calabi-Yau manifolds, mirror symmetry, mathematical aspects of string theory (with the theoretical physics group), derived categories
  • Geometric Invariant Theory
  • Gromov-Witten invariants, moduli of curves
  • calibrated geometry, exceptional holonomy, special Lagrangians
  • geometric analysis, nonlinear elliptic PDE, geometric flows.