Theses  Department of Mathematics
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Characteristic bisets and local fusion subsystems
(Bilkent University, 201809)Fusion systems are categories that contain the plocal structure of a finite group. Bisets are sets endowed with two coherent group actions. We investigate the relation between fusion systems and bisets in this thesis. Fusion ... 
Which algebraic K3 surfaces cover an enriques surface
(Bilkent University, 201809)We partially determine the necessary and su cient conditions on the entries of the intersection matrix of the transcendental lattice of algebraic K3 surface with Picard number 18 (X) 19 for the surface to doubly ... 
The pandemic fusion system for endomorphism algebras of ppermutation modules
(Bilkent University, 201809)During the 1980's Puig developed a new approach to modular representation theory, introducing new plocal invariants and thereby extending Green's work on Galgebras. We investigate the Puig category, commenting on its ... 
A conjecture on squarezero upper triangular matrices and Carlsson's rank conjecture
(Bilkent University, 201809)A wellknown conjecture states that if an elementary abelian pgroup acts freely on a product of spheres, then the rank of the group is at most the number of spheres in the product. Carlsson gives an algebraic version ... 
Chain maps between Gruenberg resolutions
(Bilkent University, 201808)Let G be a finite group. For a given presentation of G = hFRi, Gruenberg gives a construction of a projective resolution for Z as a ZGmodule. This resolution, which is called Gruenberg resolution, only depends on the ... 
Dilations of doubly invariant kernels valued in topologically ordered * spaces
(Bilkent University, 201807)An ordered *space Z is a complex vector space with a conjugate linear involution *, and a strict cone Z+ consisting of self adjoint elements. A topologically ordered *space is an ordered *space with a locally convex ... 
Zero sets of analytic function spaces on the unit disk
(Bilkent University, 201807)We survey some known results on the zero sets of two families of analytic function spaces and another single space de ned on the unit disk in the complex plane. We investigate mostly the basic properties of the zero sets ... 
Codes on fibre products of ArtinSchreier and Kummer coverings of the projective line
(Bilkent University, 200208)In this thesis, we study smooth projective absolutely irreducible curves defined over finite fields by fibre products of ArtinSchreier and Kummer coverings of the projective line. We construct some curves with many rational ... 
Stochastic analysis of shortrate modeling: which approach yields a better fit to data?
(Bilkent University, 201710)This thesis investigates the extent to which the two of the most common onefactor shortrate models are able to describe the market behavior of risk free Turkish treasuries for the post2005 period. The investigated ... 
Geodesic connectedness and completeness of twice warped products
(Bilkent University, 201709)We introduce the semiRiemannian geometry. We give some results about Riemannian and Lorentzian manifolds. We explained the Lorentzian causality. We focus on the causality of spacetimes. We de ne the Lorentzian distance. ... 
The MongeKantorovich mass transportation problem
(Bilkent University, 201709)The Monge mass transportation problem was stated by French Mathematician, G. Monge [6]. After that Soviet Mathematician Leonid Kantorovich [4] published a relaxed version of the problem, namely the MongeKantorovich ... 
Representations of symmetric groups and structures of Lie algebra
(Bilkent University, 201708)The aim of this thesis construct structure of Free Lie Algebra L(V ) generated by nite dimensional vector space V and decompose into irreducible components of a given degree n. To splits into irreducible component, ... 
Extremal problems and bergman projections
(Bilkent University, 201707)Studying extremal problems on Bergman spaces is rather new and techniques used are usually specific to the problem to be solved. However, a 2014 paper by T. Ferguson developed a systematic method using Bergman projections ... 
Minimal surfaces on threedimensional Walker manifolds
(Bilkent University, 201706)Lorentzian Geometry has shown to be very useful in a wide range of studies including many diverse research elds, especially in the theory of general relativity and mathematical cosmology. A Walker manifold descends from ... 
Asymptotics of extremal polynomials for some special cases
(Bilkent University, 201705)We study the asymptotics of orthogonal and Chebyshev polynomials on fractals. We consider generalized Julia sets in the sense of Br uckB uger and weakly equilibrium Cantor sets which was introduced in [62]. We give ... 
Extension problem and bases for spaces of infinitely differentiable functions
(Bilkent University, 201704)We examine the Mityagin problem: how to characterize the extension property in geometric terms. We start with three methods of extension for the spaces of Whitney functions. One of the methods was suggested by B. S. Mityagin: ... 
Monoid actions, their categorification and applications
(Bilkent University, 201701)We study actions of monoids and monoidal categories, and their relations with (co)homology theories. We start by discussing actions of monoids via biactions. We show that there is a welldefined functorial reverse action ... 
Deformation classes of singular quartic surfaces
(Bilkent University, 201701)We study complex spatial quartic surfaces with simple singularities and give their classication up to equisingular deformation. Simple quartics are K3surfaces and as such they can be studied by means of the global Torelli ... 
On the Nẹ́ronseveri lattice of Delsarte surfaces
(Bilkent University, 201610)The Nẹ́ronSeveri group, NS(X), of a given (nonsingular projective) variety, X, is defined in only algebrogeometric terms, however it is also known to be an arithmetic invariant. So it is an important study that helps ... 
Numerical study of orthogonal polynomials for fractal measures
(Bilkent University, 201607)In recent years, potential theory has an essential effect on approximation theory and orthogonal polynomials. Basic concepts of the modern theory of general orthogonal polynomials are described in terms of Potential Theory. ...