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 ...
  • Alexander modules of trigonal curves 

    Üçer, Melih (Bilkent University, 2021-01)
    We classify the monodromy Alexander modules of non-isotrivial trigonal curves.
  • 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, ...
  • Deformations of some biset-theoretic categories 

    Öğüt, İsmail Alperen (Bilkent University, 2020-09)
    We define the subgroup category, a category on the class of finite groups where the morphisms are given by the subgroups of the direct products and the composition is the star product. We also introduce some of its ...
  • 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 ...
  • Generic initial ideals of modular polynomial invariants 

    Danış, Bekir (Bilkent University, 2020-07)
    We study the generic initial ideals (gin) of certain ideals that arise in modular invariant theory. For all the cases where an explicit generating set is known, we calculate the generic initial ideal of the Hilbert ideal ...
  • 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 ...
  • Cohomology of infinite groups realizing fusion systems 

    Gündoğan, Muhammed Said (Bilkent University, 2019-09)
    Given a fusion system F defined on a p-group S, there exist infinite group models, constructed by Leary and Stancu, and Robinson, that realize F. We study these models when F is a fusion system of a finite group G. If ...
  • Canonical induction, Green functors, lefschetz invariant of monomial G-posets 

    Mutlu, Hatice (Bilkent University, 2019-06)
    Green functors are a kind of group functor, rather like Mackey functors, but with a further multiplicative structure. They are defined on a category whose objects are finite groups and whose morphisms are generated by ...
  • 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 ...
  • 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, 2018-07)
    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 ...
  • Dilations of doubly invariant kernels valued in topologically ordered *- spaces 

    Ay, Serdar (Bilkent University, 2018-06)
    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 ...

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