Theses  Department of Mathematics
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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. ... 
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. 
Concrete sheaves and continuous spaces
(Bilkent University, 2015)In algebraic topology and differential geometry, most categories lack some good ”convenient” properties like being cartesian closed, having pullbacks, pushouts, limits, colimits... We will introduce the notion of continuous ... 
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 ...