The duality paradigm for compact Lie groups, past and present
The duality paradigm for compact Lie groups, past and present

Akshay Venkatesh, IAS & Princeton
Fine Hall 314
It is a remarkable and nontrivial fact that there is a duality on the set of compact connected Lie groups; this interchanges, for example, the group of 2x2 unitary matrices of determinant 1, and the group of rotations in three real dimensions. This duality emerged in mathematics in the 1960s ("Langlands duality"), and independently in physics in the 1970s ("electricmagnetic duality"). I will give a gentle introduction to this duality, without assuming background in Lie theory, and say a few sketchy words about the role it plays in various settings. I will then say a little about my recent work with BenZvi and Sakellaridis where we seek to incorporate into the duality spaces upon which the groups act.