Riemann functions, their weights, and modeling Riemann-Roch formulas as Euler characteristics
department or school: Science, Faculty of
department or school: Mathematics, Department of
data provider: DSpace
degree campus: UBCV
creator: Nicolas, Folinsbee
issued: 2022-01-07T19:32:34Z
issued: 2022
related degree: Doctor of Philosophy - PhD
degree grantor: University of British Columbia
description: In this thesis, we discuss modelling with (virtual) k-diagrams a class of functions from â¤â¿ to â¤, which we call Riemann functions, that generalize the graph Riemann-Roch rank functions of Baker and Norine. The graph Riemann-Roch theorem has seen significant activity in recent years, however, as of yet, there is not a satisfactory homological interpretation of this theorem. This may be viewed as disappointing given the rich homological theory contained in the classical Riemann-Roch theorem. For a graph Riemann-Roch function, we will be able to express the associated graph Riemann-Roch formula as a (virtual) Euler characteristic of the modelling (virtual) k-diagram. From the development of this approach, we obtain a new formula for computing the graph Riemann-Roch rank of the complete graph Kn.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/80602
note: Riemann Functions, Their Weights,and Modeling Riemann-RochFormulas as Euler CharacteristicsbyNicolas FolinsbeeB.Sc., McGill University, 2014M.Sc., McGill University, 2015A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Mathematics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)December 2021© Nicolas Folinsbee 2021The following individuals certify that they have read, and recommendto the Faculty of Graduate and Postdoctoral Studies for acceptance, thedissertation entitled:Riemann Functions, Their Weights, and Modeling Riemann-RochFormulas as Euler Characteristicssubmitted by Nicolas Folinsbee in partial fulfillment of the requirementsfor the degree of Doctor of Philosophy in Mathematics.Examining Committee:Professor Joel Friedman, Computer Science, UBCSupervisorProfessor Kalle Karu, Mathematics, UBCSupervisory Committee MemberProfessor Brian Marcus, Mathematics, UBCUniversity ExaminerProfessor Lutz Lampe, ECE, UBCUniversity ExaminerAdditional Supervisory Committee Members:Professor Lior Silberman, Mathematics, UBCSupervisory Committee MemberiiAbstractIn this thesis, we discuss modelling with (virtual) k-diagrams a class offunctions from Zn to Z, which we call Riemann functions, that generalizethe graph Riemann-Roch rank functions of Baker and Norine. The graphRiemann-Roch theorem has seen significant activity in recent years, how-ever, as of yet, there is not a satisfactory homological interpretation of thistheorem. This may be viewed as disappointing given the rich homologi-cal theory contained in the classical Riemann-Roch theorem. For a graphRiemann-Roch function, we will be able to express the associated graphRiemann-Roch formula as a (virtual) Euler characteristic of the modelling(virtual) k-diagram. From the development of this approach, we obtain anew formula for computing the graph Riemann-Roch rank of the completegraph Kn.iiiLay SummaryIn mathematics, a duality…
has type: Thesis/Dissertation
date issued: 2022-05
is shown at: 10.14288/1.0406221
language: eng
degree discipline: Mathematics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Friedman, Joel, 1962-
type: Text
identifier URI: http://hdl.handle.net/2429/80602