The group in Geometry and Topology does research in diverse areas of: 

• Algebraic Geometry - (enumerative algebraic geometry, moduli theory, Donaldson-Thomas theory, derived algebraic & differential geometry, derived categories & stability conditions, and logarithmic geometry)
• Contact and Symplectic Geometry 
• Differential Geometry - (conformal geometry) 
• Low-dimensional Topology - (braid theory, hyperbolic 3-manifolds, knot theory)
• Quantum Topology - (knot homology theory, hall algebras, categorical methods)
• Topological Data Analysis