Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Stacky formulations of Einstein gravity
Download
thesis_kib.pdf
Date
2021-5-28
Author
Berktav, Kadri İlker
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
302
views
129
downloads
Cite This
This is a thesis on higher structures in geometry and physics. Indeed, the current work involves an extensive and relatively self-contained investigation of higher categorical and stacky structures in (vacuum) Einstein gravity with vanishing cosmological constant. In the first three chapters of the thesis, we shall provide a realization of the moduli space of Einstein’s field equations as a certain higher space (a stack). In this part of the thesis, the first aim is to present the construction of the moduli stack of vacuum Einstein gravity with vanishing cosmological constant in an n-dimensional setup. In particular, we shall be interested in the moduli space of 3D Einstein gravity on specific Lorentzian spacetimes. With this spirit, the second goal of this part is to show that once it exists, the equivalence of 3D quantum gravity with gauge theory in a particular setup, in fact, induces an isomorphism between the corresponding moduli stacks where the setup involves Lorentzian spacetimes of the form Mx R with M being a closed Riemann surface of genus g > 1. For our purposes, we shall employ a particular treatment that is essentially based on a formulation of stacks in the language of homotopy theory. The remainder of the thesis, on the other hand, is designed as a detailed survey on formal moduli problems, and it is particularly devoted to formalizing specific Einstein gravities in the language of formal moduli problems and L_infinity-algebras. Such an approach allows us to encode further higher structures in the theory if needed. To be more precise, this leads to the realization of the space of fields as a certain higher/derived stack (a formal moduli problem) endowed with more sensitive higher structure (encoding the possible higher symmetries/equivalences in the theory) once we ask the theory to possess higher symmetries. As a particular example, we use this approach to formulate specific 3D Einstein-Cartan-Palatini gravity. In addition, using local models for such higher structures and the algebra of functions on these higher spaces, we intend to study the algebraic structure of observables of 3D Einstein-Cartan-Palatini gravity as well.
Subject Keywords
Derived/homotopical algebraic geometry
,
Category theory
,
Higher structures
,
Higher spaces
,
Stacks
,
Formal moduli problems
,
Classical/quantum 3D Einstein gravity
URI
https://hdl.handle.net/11511/91055
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
Massive higher derivative gravity theories
Güllü, İbrahim; Tekin, Bayram; Department of Physics (2011)
In this thesis massive higher derivative gravity theories are analyzed in some detail. One-particle scattering amplitude between two covariantly conserved sources mediated by a graviton exchange is found at tree-level in D dimensional (Anti)-de Sitter and flat spacetimes for the most general quadratic curvature theory augmented with the Pauli-Fierz mass term. From the amplitude expression, the Newtonian potential energies are calculated for various cases. Also, from this amplitude and the propagator structu...
Finsler geometry and its applications to electromagnetism
Çağıl, Ayşe; İpekoğlu, Yusuf; Department of Physics (2003)
In this thesis Finsler geometry is extensively reviewed. The geometrization of fields by a Finslerian approach is considered. Also unification of electrodynamics and gravitation with suitable Finslerian metrics is examined.
Hilbert functions of gorenstein monomial curves
Topaloğlu Mete, Pınar; Arslan, Sefa Feza; Department of Mathematics (2005)
The aim of this thesis is to study the Hilbert function of a one-dimensional Gorenstein local ring of embedding dimension four in the case of monomial curves. We show that the Hilbert function is non-decreasing for some families of Gorenstein monomial curves in affine 4-space. In order to prove this result, under some arithmetic assumptions on generators of the defining ideal, we determine the minimal generators of their tangent cones by using the standard basis and check the Cohen-Macaulayness of them. Lat...
Effects of using manipulatives on seventh grade students' achievement in transformation geometry and orthogonal views of geometric figures
Enki, Kerim; Haser, Çiğdem; Department of Elementary Science and Mathematics Education (2014)
The purpose of the present study was to investigate the effects of using manipulatives on seventh grade students’ achievement in transformation geometry and orthogonal views of geometric figures. This study also aimed to investigate students’ views about using manipulatives. The study was conducted in one elementary school in Keçiören district of Ankara in the Spring semester of 2012-2013 academic year. The study employed a static group pretest-posttest research design with 73 seventh grade students. Two cl...
The moduli of surfaces admitting genus two fibrations over elliptic curves
Karadoğan, Gülay; Önsiper, Mustafa Hurşit; Department of Mathematics (2005)
In this thesis, we study the structure, deformations and the moduli spaces of complex projective surfaces admitting genus two fibrations over elliptic curves. We observe that, a surface admitting a smooth fibration as above is elliptic and we employ results on the moduli of polarized elliptic surfaces, to construct moduli spaces of these smooth fibrations. In the case of nonsmooth fibrations, we relate the moduli spaces to the Hurwitz schemes H(1,X(d),n) of morphisms of degree n from elliptic curves to the ...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
K. İ. Berktav, “Stacky formulations of Einstein gravity,” Ph.D. - Doctoral Program, Middle East Technical University, 2021.