UBC Mathematics Colloquium: Harold Williams

The discovery of so-called canonical (or crystal) bases of quantum groups by Lusztig and Kashiwara was one of the major milestones of Lie theory during the past three decades. The larger theory of canonical bases that grew out of their work (and others') has continually revealed surprising connections to other areas of mathematics such as algebraic and symplectic geometry. In this talk we sample some of these connections, for example to the geometry of character varieties of surfaces, and explain how ideas from theoretical physics provide an organizing framework for many mathematically disparate results. A central role is played by the flexible combinatorial language of cluster algebras, which provides a useful lingua franca for the subject.