Por Marko Stošić (Departamento de Matemática - Ciências ULisboa).
Knot theory historically started as one of the fundamental topics in low-dimensional topology. Nevertheless, through numerous invariants discovered in recent decades, knots became perfect language for bridging different fields of mathematics and physics, including quantum groups, statistical models, representation theory, von Neumann algebras, homological algebras, quantum field theory, string theory, etc… In this talk I will give a general overview of the general aspects of some of knot invariants, in particular quantum polynomial invariants, and homological knot invariants, as well as some recent surprising applications of these invariants in enumerative combinatorics and number theory.