Dept. of Mathematics  Master's degree
Recent Submissions

Finite psubgroups of Sp(n)
(Bilkent University, 202109)Hikari [1] classiﬁes all ﬁnite psubgroups of simple algebras, and Banieqbal [2] classiﬁes the ﬁnite subgroups of 2×2 matrices over a division algebra of characteristic zero. In this thesis, we give a new proof for the ... 
The geometry of sheaves on sites
(Bilkent University, 202101)In this work, we study doing geometry on sheaves on sites. Categories of our sites consist of objects that are building blocks for a given geometry. Generalized spaces then will be sheaves on these sort of sites. Next we ... 
Lebesgue constants on cantor type sets
(Bilkent University, 202009)The properties of compact subsets of the real line which are in the class of Bounded Lebesgue Constants (BLC) are investigated. Knowing that any such set must have 1dimensional Lebesgue measure zero and nowhere density, ... 
Constructions and simplicity of the Mathieu groups
(Bilkent University, 202008)Of the 26 sporadic finite simple groups, 5 were discovered by E. Mathieu in 1861 and 1873 [1], [2]. These Mathieu groups are the focus of this thesis, where we will prove their simplicity using elementary methods. E. ... 
Mackey decomposition for Brauer pairs
(Bilkent University, 202008)For a ﬁnite group G and an algebraically closed ﬁeld k of characteristic p, a kalgebra A with a Gaction is called a Galgebra. A pair (P,c) such that P is a psubgroup of G and c is a block idempotent of the Galgebra ... 
Analysis on selfsimilar sets
(Bilkent University, 202008)Selfsimilar sets are one class of fractals that are invariant under geometric similarities. In this thesis, we study on selfsimilar sets. We give the deﬁnition of a selfsimilar set K and present the proof the existence ... 
Effect of time delays on the convergence speed of consensus dynamics
(Bilkent University, 202001)We discuss consensus problems under time delays. The presence of time delays results in an inﬁnitedimensional system rather than a system of ordinary differential equations. It has been shown that information transmission ... 
Which algebraic K3 surfaces doubly cover an enriques surface: a computational approach
(Bilkent University, 201902)The relationship between K3 Surfaces and Enriques Surfaces is known to mathematicians for the last 30 years. We examined this relationship from a lattice theoretical point of view by looking at transcendental lattice of ... 
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 ... 
Chain maps between Gruenberg resolutions
(Bilkent University, 201807)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 ... 
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 ... 
Stochastic analysis of shortrate modeling: which approach yields a better fit to data?
(Bilkent University, 201709)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, 201707)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 ... 
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 ...