Speaker: Matteo Parisi
Abstract: Recent studies of scattering amplitudes—the probabilities of particle interactions in quantum field theory—have led to remarkable connections with algebraic combinatorics and geometry. A striking example is the amplituhedron, a novel object whose `volume’ gives scattering amplitudes in planar N=4 super Yang-Mills theory. Computing this volume requires decomposing (or tiling) the amplituhedron into smaller pieces (or tiles) and summing their volumes. In this talk, I will introduce the amplituhedron, explain its ties to the Grassmannian and total positivity, and discuss our recent advances in understanding its tiles, tilings, and novel connections with cluster algebras.
Abstract: Recent studies of scattering amplitudes—the probabilities of particle interactions in quantum field theory—have led to remarkable connections with algebraic combinatorics and geometry. A striking example is the amplituhedron, a novel object whose `volume’ gives scattering amplitudes in planar N=4 super Yang-Mills theory. Computing this volume requires decomposing (or tiling) the amplituhedron into smaller pieces (or tiles) and summing their volumes. In this talk, I will introduce the amplituhedron, explain its ties to the Grassmannian and total positivity, and discuss our recent advances in understanding its tiles, tilings, and novel connections with cluster algebras.