Date of Award

Winter 12-15-2016

Author's School

Graduate School of Arts and Sciences

Author's Department

Mathematics

Degree Name

Doctor of Philosophy (PhD)

Degree Type

Dissertation

Abstract

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.

Language

English (en)

Chair and Committee

Matthew Kerr

Committee Members

Matthew Kerr, Xiang Tang, Renato Feres, John Shareshian

Comments

Permanent URL: https://doi.org/10.7936/K74Q7SD8

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