Abstract: 

One of the central foci of representation theory in the 20th century was the representation theory of Lie algebras, starting with finite dimensional algebras and expanding to a rich, but still mysterious infinite dimensional theory.  In this century, we realized that this was only one special case of a bigger theory, with new sources of interesting non-commutative algebras whose representations we’d like to study such as Cherednik algebras.  In mathematical terms, we could connect these to symplectic resolutions of singularities, but more intriguing explanation is that they arise 3-d quantum field theories.   I’ll try to provide an overview about what’s known about this topic, and what we’re still confused about.

Bio:

Ben Webster is an Associate Professor in Pure Mathematics at the University of Waterloo, and an Associate Faculty member at Perimeter Institute.  His areas of expertise include geometric representation theory, diagrammatic algebra and low-dimensional topology.  He received his BA in 2002 from Simon's Rock College.  He received his Ph.D. in 2007 from the University of Calfornia, Berkeley and went on to postdoctoral positions at the Institute for Advanced Study and MIT before coming to Waterloo in 2017.  He's been the recipient of an NSF CAREER award and an Alfred P. Sloan fellowship.

Video: http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Representation_theory_and_a_little_bit_of_quantum_field_theory.html