<mods:mods xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-7.xsd"><mods:titleInfo><mods:title>Landau Singularities and Positive Geometries</mods:title></mods:titleInfo><mods:name type="personal"><mods:namePart>Stanojevic, Stefan</mods:namePart><mods:role><mods:roleTerm type="text">creator</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Spradlin, Marcus</mods:namePart><mods:role><mods:roleTerm type="text">Advisor</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Jevicki, Antal</mods:namePart><mods:role><mods:roleTerm type="text">Reader</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Alexander, Stephon</mods:namePart><mods:role><mods:roleTerm type="text">Reader</mods:roleTerm></mods:role></mods:name><mods:name type="corporate"><mods:namePart>Brown University. Department of Physics</mods:namePart><mods:role><mods:roleTerm type="text">sponsor</mods:roleTerm></mods:role></mods:name><mods:originInfo><mods:copyrightDate>2020</mods:copyrightDate></mods:originInfo><mods:physicalDescription><mods:extent>9, 109 p.</mods:extent><mods:digitalOrigin>born digital</mods:digitalOrigin></mods:physicalDescription><mods:note type="thesis">Thesis (Ph. D.)--Brown University, 2020</mods:note><mods:genre authority="aat">theses</mods:genre><mods:abstract>This work studies the analytical structure of scattering amplitudes in a class of toy models, &#13;
from the perspective of novel geometrical structures underlying scattering amplitudes, and &#13;
utilizing discrete mathematics. We find the set of all-loop n - point Landau singularities of the &#13;
first type arising in any massless planar theory using graph operations inspired by the theory of electrical circuits.&#13;
We also describe how to find the set of possible branch points of amplitudes at any fixed loop&#13;
order and all particle multiplicities in planar N = 4 SYM theory, using the information contained&#13;
in the boundaries of the amplituhedra. Along the way, we devise a method for classifying the&#13;
boundaries of amplituhedra for any loop order L and helicity k. We determine the branch points&#13;
of all two-loop NMHV amplitudes by solving the Landau equations for the relevant configurations&#13;
and are led thereby to a conjecture for the symbol alphabets of all such amplitudes. The study&#13;
of amplituhedra is then pushed beyond the realm of N = 4 SYM theory. We provide an efficient&#13;
recursive formula to compute the canonical forms of arbitrary d-dimensional simple polytopes, and&#13;
illustrate our method via an application to Stokes polytopes, related to scalar theory with quartic coupling.</mods:abstract><mods:subject authority="fast" authorityURI="http://id.worldcat.org/fast" valueURI="http://id.worldcat.org/fast/01085105"><mods:topic>Quantum field theory</mods:topic></mods:subject><mods:subject authority="fast" authorityURI="http://id.worldcat.org/fast" valueURI="http://id.worldcat.org/fast/00946584"><mods:topic>Graph theory</mods:topic></mods:subject><mods:subject authority="fast" authorityURI="http://id.worldcat.org/fast" valueURI="http://id.worldcat.org/fast/01070819"><mods:topic>Polytopes</mods:topic></mods:subject><mods:language><mods:languageTerm authority="iso639-2b">English</mods:languageTerm></mods:language><mods:recordInfo><mods:recordContentSource authority="marcorg">RPB</mods:recordContentSource><mods:recordCreationDate encoding="iso8601">20200720</mods:recordCreationDate></mods:recordInfo><mods:accessCondition type="rights statement" xlink:href="http://rightsstatements.org/vocab/InC/1.0/">In Copyright</mods:accessCondition><mods:accessCondition type="restriction on access">Collection is open for research.</mods:accessCondition><mods:typeOfResource authority="primo">dissertations</mods:typeOfResource></mods:mods>