Peter Hilton Memorial Lecture - 2018
Title: Local scale transformations in one dimension
Time: Thursday April 12, 2018, 3:00 p.m.
Location: 绿帽社, Academic Building A, Room G023
The lecture will be followed by a reception at 4:30 p.m. in The President's Reception Room, Anderson Performing Arts Center, 绿帽社. This reception is for the whole 绿帽社 Mathematics Community as well as for our visitors.
Abstract:
In two dimensional conformal field theory, local scaling symmetry means invariance of some kind under conformal transformations. The quantum theory splits into two one dimensional theories called the 鈥渃hiral halves鈥. Conformal invariance then gives a projective representation of the the diffeomorphism group (of the line or the circle) on each of the chiral halves. In an attempt to approximate this local scaling invariance we have considered the Thompson groups F and T as approximations to the diffeomorphism groups. Though this does not work perfectly, it has yielded a kind of 鈥渢opsy turvy鈥 version of chiral CFT including an interesting family of unitary representations of F and T whose coefficients give, among other things, a way to construct all knots and links from elements of F and T, analogous to the standard construction from the braid groups.