Advanced School on Geometric Group Theory and Low-Dimensional Topology - Recent Connections and Advances

Explore cutting-edge research in geometric group theory and low-dimensional topology through this advanced school featuring 22 hours and 54 minutes of specialized lectures. Delve into the intersection of geometry, topology, and group theory through comprehensive coverage of virtually special groups and cube complexes, hyperbolic 3-manifolds, mapping class groups, and curve complexes. Master higher Teichmüller theory and geometric structures while examining left orderability, L-spaces, and their applications to 3-manifolds. Investigate dynamics on Teichmüller space and moduli space through expert presentations on topics including Windows cores and skinning maps, higher rank Morse lemmas, quasi-Hitchin symplectic Anosov representations, and orderability in Dehn filling. Study advanced concepts such as Liouville currents and complex structures for Hitchin representations, spherical metrics on conical surfaces, geodesic currents and length functions, Veech groups and cutting sequences, and the Virtual Fibering Conjecture. Examine automorphisms of right-angled Artin groups, curve counting on surfaces, exotic compact quotients of PSL(2,C), and renormalized volume of quasifuchsian manifolds. Analyze totally geodesic subvarieties in moduli spaces, hierarchically hyperbolic spaces and their boundaries, ultralimits of maximal representations, and slope detection in 3-manifolds. Explore character varieties of knots and their reductions mod p, proper affine actions of right-angled Coxeter groups, quasi-isometric rigidity of convex-cocompact Kleinian groups, rationality and volume growth in polynomial ranges, and RFRS for congruence covers.