Quantum Groups And Their Invariant Theory

Abstract

The focus of this research is on algebraic manifestations of quantum symmetries, more specifi- cally from the point of view of homological algebra, representation theory, category theory, and noncommutative algebraic geometry. The notion of a group describes symmetry in mathemat- ics. In recent decades, certain “quantum” examples include subfactors, quantum groups, Hopf algebras,and topological phases of matter. These mathematical objects have applications in the diverse range of settings across mathematics and physics, including quantum invariant of links and 3-manifolds, representation theory, condensed matter physics,topological phases of matter, and quantum information.