Abstract: There are tantalising analogies between the theory of mapping class groups and other classes of groups, and as a result the well-developed study of mapping class groups has been an important model to mimic in other parts of group theory. I'll try to describe how some ideas from geometric group theory have been imported into the study of groups arising in homological algebra and representation theory.

Bio: I grew up in Texas, and got my PhD from Yale in 2007. I have worked at the Australian National University since 2012. I am a Professor in the Mathematical Sciences Institute at the Australian National University in Canberra, Australia.

I work on geometric representation theory and categorification. Most of my work involves interactions between representation theory and low-dimensional topology (braids, knot homologies), symplectic algebraic geometry (quiver varieties, Hilbert schemes), and algebraic combinatorics (symmetric functions, hyperplane arrangements).