Date of Award
Doctor of Philosophy (PhD)
Chapter 1 contains background material on higher Chow groups, KLM formula and Feynman integrals. In Chapter 2, we construct explicit bases for these extension classes mapping to zeta values. In Chapter 4, we study the Feynman integral of the three spoke wheel graph, reinterpret it as an image of regulator using higher Abel-Jacobi maps and theoretically prove that it is a rational multiple of zeta three. In Chapter 5, a reflexive graph polytope based on the graph polynomial is constructed. In Chapter 6, to generalize the results beyond wheel with three spokes, a criterion is given on the vanishing of graph symbols. An essential blow-up construction is reinterpreted in toric language to reveal the ambient space's combinatorial structure.
Chair and Committee
Matthew Kerr, Xiang Tang, Renato Feres, John Shareshian
Yang, Yu, "Explicit bases of motives over number fields with application to Feynman integrals" (2016). Arts & Sciences Electronic Theses and Dissertations. 1017.