Events by date

Title: Diagrammatic boundary calculus for Wilson loop diagrams

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm.

Abstract: This talk is about a different part of the quantum field theory story than I usually talk about.  Wilson loop diagrams can be used to index amplitudes in a theory known as N=4 SYM.  Suitably nice Wilson loop diagrams are also associated to positroids.  For both mathematical and physical reasons it would be nice to have a diagrammatic understanding of the boundaries of the positroid cells of all co-dimensions.  While we do not yet have a full understanding, we can build many boundaries with certain diagrammatic moves.

Joint work with Susama Agarwala and Colleen Delaney.

Title: A closure lemma for tough graphs and Hamiltonian ideals

Abstract: The closure of a graph $G$ is the graph $G^*$ obtained from $G$ by repeatedly adding edges between pairs of non-adjacent vertices whose degree sum is at least $n$, where $n$ is the number of vertices of $G$. The well-known Closure Lemma proved by Bondy and Chv\'atal states that a graph $G$ is Hamiltonian if and only if its closure $G^*$ is. This lemma can be used to prove several classical results in Hamiltonian graph theory. We prove a version of the Closure Lemma for tough graphs.