Cameron Marcott
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Cancellation of spurious poles in N=4 SYM: physical and geometric Open
This paper shows that not only do the codimension one spurious poles of $N^k MHV$ tree level diagrams in N=4 SYM theory cancel in the tree level amplitude as expected, but their vanishing loci have a geometric interpretation that is tightl…
Combinatorics of Grassmannian Decompositions Open
This thesis studies several combinatorially defined families of subsets of the Grassmannian. We introduce and study a family of subsets called “basis shape loci” associated to transversal matroids. Additionally, we study the Deodhar and po…
Basis shape loci and the positive Grassmannian Open
A basis shape locus takes as input data a zero/nonzero pattern in an $n \times k$ matrix, which is equivalent to a presentation of a transversal matroid. The locus is defined as the set of points in the Grassmannian of $k$ planes in $\math…
Wilson loops in SYM $N=4$ do not parametrize an orientable space Open
In this paper we explore the geometric space parametrized by (tree level) Wilson loops in SYM $N=4$. We show that, this space can be seen as a vector bundle over a totally non-negative subspace of the Grassmannian, $\mathcal{W}_{k,cn}$. Fu…
Positroids have the Rayleigh property Open
The Rayleigh property is a negative correlation property of electrical networks, which was generalized to matroids by Choe and Wagner. We prove that positroids, a class of matroid introduced by Postnikov which have seen many recent applica…