The Amplituhedron BCFW Triangulation
Abstract: The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the […]
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Invariant theory for maximum likelihood estimation
Abstract: I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum […]
Equiangular lines and regular graphs
Abstract: In 1973, Lemmens and Seidel asked to determine N_alpha(r), the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently, this problem has been almost completely settled when […]
Rational Polypols
Abstract: Eugene Wachspress introduced polypols as real bounded semialgebraic sets in the plane that generalize polygons. He aimed to generalize barycentric coordinates from triangles to arbitrary polygons and further to […]
Greedy maximal independent sets via local limits
Abstract: The random greedy algorithm for finding a maximal independent set in a graph has been studied extensively in various settings in combinatorics, probability, computer science, and chemistry. The algorithm builds […]
Moduli space of tropical curves, graph Laplacians and physics
Abstract: I will first review the construction of the moduli space of tropical curves (or metric graphs), and its relation to graph complexes. The graph Laplacian may be interpreted as a […]
Flip processes
Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all […]
BCFW recursion relations and non-planar positive geometry
Abstract: There is a close connection between the scattering amplitudes in planar N=4 SYM theory and the cells in the positive Grassmannian. In the context of BCFW recursion relations the tree-level […]
Some combinatorics of Wilson loop diagrams
Abstract: Wilson loop diagrams can be used to study amplitudes in N=4 SYM. I will set them up and talk about some of their combinatorial aspects, such as how many […]
Algebraic Statistics with a View towards Physics
Abstract: We discuss the algebraic geometry of maximum likelihood estimation from the perspective of scattering amplitudes in particle physics. A guiding examples the moduli space of n-pointed rational curves. The scattering […]
The threshold for stacked triangulations
Abstract: Consider a bootstrap percolation process that starts with a set of `infected’ triangles $Y \subseteq \binom{}3$, and a new triangle f gets infected if there is a copy of […]
Hypergraph Matchings Avoiding Forbidden Submatchings
Abstract: In 1973, Erdős conjectured the existence of high girth (n,3,2)-Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erdős’ conjecture. Just […]