Title: Trees, chord diagrams and the renormalization group equation
| Speaker: | Karen Yeats |
| Affiliation: | Simon Fraser University |
| Room: | MC 5417 |
Abstract: How far can we get in understanding perturbative expansions in quantum field theory combinatorially?
This understanding begins with a connection between classes of rooted trees and Dyson-Schwinger equations in physics. Then I will discuss a family of such equations where we understand the perturbative expansion precisely via an expansion indexed by chord diagrams. The renormalization group equation of physics corresponds in this context to a classical recurrence of chord diagrams. Finally, looking more generally, we lose precise control on the whole expansion but retain a combinatorial understanding of the renormalization group equation by returning to rooted trees.