Title: Poset subHopf algebras from growth models in causal set theory and quantum field theory
| Speaker: | Karen Yeats |
| Affiliation: | University of Waterloo |
| Location: | MC 5501 and Zoom - please contact Oliver Pechenik for the Zoom link |
Abstract: In a story some of you have heard from me before, we get subHopf algebras of the Connes-Kreimer Hopf algebra of rooted trees from certain simple tree classes which correspond to solutions to combinatorial analogues of Dyson-Schwinger equations in quantum field theory. Another important subHopf algebra of the Connes-Kreimer Hopf algebra is the Connes-Moscovici Hopf algebra which can be viewed as coming from rooted trees grown by adding leaves.
On the other hand, causal set theory is an approach to quantum gravity where in place of spacetime we have a locally finite poset with the poset relation interpreted as the causal relation between spacetime points. The classical sequential growth (CSG) model builds finite posets one element at a time with certain weights and is used in causal set theory.
I will give a common framework for all these classes/models, and discuss a new result with Stav Zalel on when certain models related to the CSG model give subHopf algebras of the poset Hopf algebra.
The presentation will be combinatorial and will not assume knowledge of causal set theory or quantum field theory.
Joint work with Stav Zalel.