Algebra

The Algebraic Combinatorics and Fundamental Physics Unit investigates new algebro-combinatorial and geometric structures underlying quantum field theory, focusing on scattering amplitudes, total positivity, amplituhedra, and cluster algebras.

Chiral representation theory unit investigates the symmetries arising in quantum field theories. More specifically, it focuses on the representation theory of infinite-dimensional Lie algebras such as Kac–Moody algebras, and more generally, on vertex algebras.

The Geometric Group Theory Unit studies the large-scale geometry of infinite groups, focusing on hyperbolic and non-positively curved spaces, growth, and projections.

Our unit studies the representation theory of algebras via tools from algebraic combinatorics. Our study largely centres around the philosophy of decomposing representations.