Abstract:
A metric graph (or Feynman graph!), G, defines a positive semi-definite quadratic form, Q, its Laplacian. The Voronoi cell associated to Q is an interesting polytope. We give a formula to determine the normal fan of the polytope from the graph. Computing the vectors that generate the fan is a crucial step when computing the tropical limits of Riemann theta functions. In string theory, this shows up when studying the alpha' expansion of worldsheet integrals at genus g>1.
About the speaker:
Hadleigh Frost is a theoretical physicist whose research focuses on algebraic and combinatorial structures arising in the computation of scattering amplitudes in quantum field theory and string theory, with particular emphasis on understanding particle scattering at both weak and strong coupling. He received his D.Phil. from the University of Oxford in 2021, subsequently held a postdoctoral position affiliated with Merton College, and is currently a member in the School of Natural Sciences at the Institute for Advanced Study (IAS) in Princeton.
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