Scattering amplitudes of stable curves

  • Jenia Tevlev (University of Massachusetts Amherst)
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Equations of hypertree divisors on the Grothendieck-Knudsen moduli space of stable rational curves, introduced by Castravet and Tevelev, appear as numerators of scattering amplitude forms for n massless particles in N=4 Yang-Mills theory in the work of Arkani-Hamed, Bourjaily, Cachazo, Postnikov and Trnka. We re-interpret and generalize leading singularities of MHV scattering amplitude forms as probabilistic Brill-Noether theory: the study of statistics of images of n marked points on a Riemann surface under a random meromorphic function. This leads to a beautiful physics-inspired geometry for various classes of algebraic curves: smooth, stable, hyperelliptic, real algebraic, etc.

22.04.21 14.01.22

Leipzig seminar on Algebra, Algebraic Geometry and Algebraic Topology

MPI for Mathematics in the Sciences Live Stream

Katharina Matschke

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