Dept. of Mathematics  Master's degree
Recent Submissions

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. ... 
On some of the simple composition factors of the biset functor of Ppermutation modules
(Bilkent University, 201607)Let k be an algebraically closed field of characteristic p, which is a prime, and C denote the field of complex numbers. Given a finite group G, letting ppk(G) denote the Grothendieck group of ppermutation kGmodules, we ... 
Geodesics of threedimensional walker manifolds
(Bilkent University, 201607)We review some basic facts of Lorentzian geometry including causality and geodesic completeness. We depict the properties of curves and planes in threedimensional Minkowski space. We deffne the Walker manifolds, that is, ... 
Homotopy colimits and decompositions of function complexes
(Bilkent University, 201607)Given a functor F : C→ GSp, the homotopy colimit hocolimCF is defined as the diagonal space of simplicial replacement of F. Let G be a finite group and F be a family of subgroups of G, the classifying space EFG can be taken ... 
Groebner basis approach in graphtheoretical problems
(Bilkent University, 201606)In the study of graphs, it is often desirable to know about the colorability properties of a given graph or whether it is planar or if it contains a Hamiltonian cycle. We consider such problems and describe corresponding ... 
On complete intersections and connectedness
(Bilkent University, 2002)In this thesis, we study the relation between connectedness and complete intersections. We describe the concept of connectedness in codimension k. We also study the basic facts about CohenMacaulay rings, and give ... 
On the minimal number of elements generating an algebraic set
(Bilkent University, 2002)In this thesis we present studies on the general problem of finding the minimal number of elements generating an algebraic set in nspace both set and ideal theoretically. 
Blocks of quotients of mackey algebras
(Bilkent University, 2015)We review a theorem by Boltje and K¨ulshammer which states that under certain circumstances the endomorphism ring EndRG(RX) has only one block. We study the double Burnside ring, the Burnside ring and the transformations ... 
Biset functors and brauer's induction theorem
(Bilkent University, 2014)We introduce two algebras on the endomorphism ring of the direct sum of character rings of groups from some collection. We prove the equality of these algebras to simplify a step in the proof of Brauer’s Induction Theorem. ... 
Kuroda's class number formula
(Bilkent University, 2007)In number theory theory, the class number of a field is a significant invariant. All over the time, people have come up with formulas for some cases and in this thesis I will discuss a proof of a class number formula for ... 
Logarithmic dimension and bases in whitney spaces
(Bilkent University, 2006)In generalization of [3] we will give the formula for the logarithmic dimension of any Cantortype set. We will demonstrate some applications of the logarithmic dimension in Potential Theory. We will construct a polynomial ... 
Complete positivity in operator algebras
(Bilkent University, 2006)In this thesis we survey positive and completely positive maps defined on operator systems. In Chapter 3 we study the properties of positive maps as well as construction of positive maps under certain conditions. In ... 
Interpolating bases in the spaces of C(formula)functions on cantortype sets
(Bilkent University, 2006)In this work by using the method of local interpolat ions suggested in [9] we construct topological bases in the spaces of CPfunctions defined on uniformly perfect compact sets of Cantor type. Elements of the basis are ... 
Applications of duality for Hp spaces
(Bilkent University, 2006) 
The extension class of a subset complex
(Bilkent University, 2006) 
The lattice of periods of a group action and its topology
(Bilkent University, 2006)In this thesis, we study the topology of the poset obtained by removing the greatest and least elements of lattice of periods of a group action. For a Gset X where G is a finite group, the lattice of periods is defined ... 
Reproducing kernel Hilbert spaces
(Bilkent University, 2005)In this thesis we make a survey of the theory of reproducing kernel Hilbert spaces associated with positive definite kernels and we illustrate their applications for interpolation problems of NevanlinnaPick type. Firstly ... 
On Gambler's ruin problem in some models
(Bilkent University, 2005)2player probability games is an important subject of probability theory. In this thesis, we considered four different twoplayer probability games. We calculated the expected value of stopping times of the games. Since ... 
Limiting Gibbs measures in some one and two dimensional models
(Bilkent University, 2005)We give the definitions of finite volume Gibbs measure and limit Gibbs states. In one dimensional Ising model with arbitrary boundary conditions we calculate correlation functions in explicit way. In one dimension, ...