Title: Subdivergence-free gluings of treesSpeaker: Jordan Long Affiliation: University of Waterloo Zoom: Contact Karen Yeats
Motivated by questions in quantum field theory, we introduce a purely combinatorial problem of counting subdivergence-free gluings of trees. We present closed-form expressions counting subdivergence-free gluings for four different families of trees, as well as an algorithm to count subdivergence-free gluings of arbitrary pairs of trees. This is joint work with Clair Dai and Karen Yeats.
Title: Counting the $c_2$ invariant on the circulant family of graphsSpeaker: Mushegh Shahinyan Affiliation: University of Waterloo Zoom: Contact Karen Yeats
The algebro-geometric invariant on Feynman Diagrams called the $c_2$ invariant is a useful tool for detecting properties of Feynman periods. We present this identity on graphs that originate from the scalar $\phi_4$-theory with a purely combinatorial perspective and go over some strategies for computing it. We will further narrow our focus onto the circulant family of graphs and present some explicit results.
Title: Abelian covering graphs and their propertiesSpeaker: Olha Silina Affiliation: University of Waterloo Zoom: Contact Karen Yeats
A covering graph is a structure obtained from a graph by ‘replacing’ every vertex with a coclique of size $r$. The main focus of this talk is connections between (spectral) characteristic of a cover and properties such as being walk- or distance- regular.