Recent Submissions

  • Characteristic bisets and local fusion subsystems 

    Tokmak, Mustafa Anıl (Bilkent University, 2018-09)
    Fusion systems are categories that contain the p-local 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 

    Sonel, Serkan (Bilkent University, 2018-09)
    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 p-permutation modules 

    Nika, Andi (Bilkent University, 2018-09)
    During the 1980's Puig developed a new approach to modular representation theory, introducing new p-local invariants and thereby extending Green's work on G-algebras. We investigate the Puig category, commenting on its ...
  • A conjecture on square-zero upper triangular matrices and Carlsson's rank conjecture 

    Şentürk, Berrin (Bilkent University, 2018-09)
    A well-known conjecture states that if an elementary abelian p-group 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 

    Fidan, Müge (Bilkent University, 2018-08)
    Let G be a finite group. For a given presentation of G = hF|Ri, Gruenberg gives a construction of a projective resolution for Z as a ZG-module. This resolution, which is called Gruenberg resolution, only depends on the ...
  • Dilations of doubly invariant kernels valued in topologically ordered *- spaces 

    Ay, Serdar (Bilkent University, 2018-07)
    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 

    Bavaş, Berk (Bilkent University, 2018-07)
    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 Artin-Schreier and Kummer coverings of the projective line 

    Shalalfeh, Mahmoud (Bilkent University, 2002-08)
    In this thesis, we study smooth projective absolutely irreducible curves defined over finite fields by fibre products of Artin-Schreier and Kummer coverings of the projective line. We construct some curves with many rational ...
  • Stochastic analysis of short-rate modeling: which approach yields a better fit to data? 

    Bulut, Mustafa (Bilkent University, 2017-10)
    This thesis investigates the extent to which the two of the most common onefactor short-rate models are able to describe the market behavior of risk free Turkish treasuries for the post-2005 period. The investigated ...
  • Geodesic connectedness and completeness of twice warped products 

    Ateşli, Begüm (Bilkent University, 2017-09)
    We introduce the semi-Riemannian geometry. We give some results about Riemannian and Lorentzian manifolds. We explained the Lorentzian causality. We focus on the causality of space-times. We de ne the Lorentzian distance. ...
  • The Monge-Kantorovich mass transportation problem 

    Demirel, İhsan (Bilkent University, 2017-09)
    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 Monge-Kantorovich ...
  • Representations of symmetric groups and structures of Lie algebra 

    Acar, Merve (Bilkent University, 2017-08)
    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 

    Özbek, Rasimcan (Bilkent University, 2017-07)
    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 three-dimensional Walker manifolds 

    Berani, Erzana (Bilkent University, 2017-06)
    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 

    Alpan, Gökalp (Bilkent University, 2017-05)
    We study the asymptotics of orthogonal and Chebyshev polynomials on fractals. We consider generalized Julia sets in the sense of Br uck-B uger and weakly equilibrium Cantor sets which was introduced in [62]. We give ...
  • Extension problem and bases for spaces of infinitely differentiable functions 

    Merpez, Zeliha Ural (Bilkent University, 2017-04)
    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 

    Erdal, Mehmet Akif (Bilkent University, 2017-01)
    We study actions of monoids and monoidal categories, and their relations with (co)homology theories. We start by discussing actions of monoids via bi-actions. We show that there is a well-defined functorial reverse action ...
  • Deformation classes of singular quartic surfaces 

    Aktaş, Çisem Güneş (Bilkent University, 2017-01)
    We study complex spatial quartic surfaces with simple singularities and give their classication up to equisingular deformation. Simple quartics are K3-surfaces and as such they can be studied by means of the global Torelli ...
  • On the Nẹ́ron-severi lattice of Delsarte surfaces 

    Kişioğlu, Mehmet (Bilkent University, 2016-10)
    The Nẹ́ron-Severi group, NS(X), of a given (non-singular projective) variety, X, is defined in only algebro-geometric 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 

    Şimşek, Ahmet Nihat (Bilkent University, 2016-07)
    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. ...

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