Low Dimensional Topology

The purpose of this summer school is to provide an overview of new advances and perspectives in low-dimensional topology, with a focus on the study of three and four dimensional manifolds, knot theory and the mapping class group of surfaces. In the recent decades, this branch of mathematics has been developing deep connections to mathematical physics (statistical mechanics, gauge theory, quantum field theory), algebra (representation theory, quantum groups) and differential geometry (symplectic, contact and hyperbolic geometry). This summer school is intended for PhD students, postdocs and researchers in topology and the above-mentioned related fields.