Recent Submissions

  • Finite p-subgroups of Sp(n) 

    Çetin, Mustafa Seyyid (Bilkent University, 2021-09)
    Hikari [1] classifies all finite p-subgroups of simple algebras, and Banieqbal [2] classi-fies 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 

    Parsizadeh, Pejman (Bilkent University, 2021-01)
    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 

    Paksoy, Yaman (Bilkent University, 2020-09)
    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 1-dimensional Lebesgue measure zero and nowhere density, ...
  • Constructions and simplicity of the Mathieu groups 

    Karakaş, Mete Han (Bilkent University, 2020-08)
    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 

    Okur, Utku (Bilkent University, 2020-08)
    For a finite group G and an algebraically closed field k of characteristic p, a k-algebra A with a G-action is called a G-algebra. A pair (P,c) such that P is a p-subgroup of G and c is a block idempotent of the G-algebra ...
  • Analysis on self-similar sets 

    Kesimal, Hayriye Sıla (Bilkent University, 2020-08)
    Self-similar sets are one class of fractals that are invariant under geometric similarities. In this thesis, we study on self-similar sets. We give the definition of a self-similar set K and present the proof the existence ...
  • Effect of time delays on the convergence speed of consensus dynamics 

    Alhassan, Mohammed Kamil (Bilkent University, 2020-01)
    We discuss consensus problems under time delays. The presence of time delays results in an infinite-dimensional 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 

    Yörük, Oğuzhan (Bilkent University, 2019-02)
    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 

    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 ...
  • Chain maps between Gruenberg resolutions 

    Fidan, Müge (Bilkent University, 2018-07)
    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 ...
  • 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 ...
  • Stochastic analysis of short-rate modeling: which approach yields a better fit to data? 

    Bulut, Mustafa (Bilkent University, 2017-09)
    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, 2017-07)
    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 ...
  • 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 ...

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