Akram Alishahi, David Gay, Peter Lambert-Cole and Gordana Matic. Low-dimensional topology focuses on the study of 3- and 4-manifolds, embedded knots and surfaces in them, their diffeomorphism groups and contact and symplectic structures on them. The central questions are about the classification and constructions of manifolds and knotted circles and surfaces in them in various geometric or algebraic setups, topology of the diffeomorphism groups (in dimension 4). Some of the most important tools our group uses are Heegaard Floer theory, Khovanov-type homology theories and trisections.
