M.S. Theses: Recent submissions

  • Maslov indices for lagrangian triplets 
    Karabatman, Ferhat. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2020., 2020.)
    In this thesis, we study the properties and an application of Maslov ternary index. By nding some special elements which generate symplectic group, we show that Maslov ternary index becomes a very important tool in the ...
  • Class number one problem 
    Kır, Harun. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.)
    In 1801, Gauss conjectured that there are exactly nine imaginary quadratic number fields with class number one, namely: Q(√−1), Q(√−2), Q(√−3), Q(√−7), Q(√−11), Q(√−19), Q(√−43), Q(√−67) and Q(√−163). This conjecture is ...
  • Inverse galois problem 
    Kırımlı, Eda. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.)
    The main focus of this thesis is so called Inverse Galois Problem. The statement of the problem is that given a finite group G, does there exist a finite Galois extension L/Q whose Galois group is G? There has been a great ...
  • Modular approcah to diophantine equations 
    Işık, Erman. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.)
    In this thesis, we study the modular approach to the Fermat’s equation xp+yp = zp, where x,y and z are co-prime integers, and p is a prime, and some generalizations. After reviewing and explaining how the modular approach ...
  • Mackey functors and fusion systems 
    İplikçi, Ayçin. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.)
    In this thesis, we present a survey for the paper [1]. We study with the biset functors representation rings and superclass functions. We define representation rings of a saturated fusion system F and F-stable elements of ...
  • Computation of grid homology 
    Taştan, Fulya. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.)
    In this thesis, the main aim is to study a combinatorial approach of knot Floer homology for a given knot K (or a link) in S3, called grid homology. We will define the bigrading structure on the chain complexes, and will ...
  • Modular representations of GL (2,p) 
    Karakurt, Turan. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.)
    In this thesis, we investigate representations of GLp2,pqby using indecomposable projective modules for GLp2,pq. Actually, this is pure module theoretic approach in parallel with [1] since we do not refer any character ...
  • Irregular sampling in shift-invariant spaces 
    Özkaya, Sadık Görkem. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2006., 2006.)
    This thesis is an exposition of the concept of localization of frames in the problem of irregular sampling in shift-invariant spaces. The given definition of the localization of a frame will appear to be equivalent to an ...
  • A survey on endo - trivial modules 
    Sert, Gözde. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.)
    In this thesis, we investigate endo-trivial modules and their classification endo trivial modules over p-groups. Endo-trivial modules were introduced by Dade [1] and appear naturally in moduler representation theory. Several ...
  • Combinatorial computation techniques for homology comordism invariants of plumbed 3-manifolds 
    Şavk, Oğuz. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.)
    We study some invariants of homology cobordism classes in dimension three. These invariants have their roots in gauge theory but are computable combinatori ally for plumbed 3-manifolds. We illustrate certain computation ...
  • Frequency independent evaluation of highly oscillatory integrals 
    Özdemir, Rıdvan. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.)
    Oscillatory integrals appear in many applications and therefore, several differ ent quadrature rules for their accurate and efficient evaluation have been proposed in the literature. The efficiency of these methods naturally ...
  • The ordinary component of l-isogeny graph of elliptic curves 
    Kaytancı, Kübra. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2017., 2017.)
    In this thesis, our aim is to understand `-volcanoes which are ordinary compo nents of `-isogeny graphs of elliptic curves over finite fields under certain conditions. In 1996, the structure of isogeny graphs of elliptic ...
  • First moment problem in longest common subsequences 
    Demirelli, Abdurrahman. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.)
    In this thesis, we investigate the properties of the longest common subsequences in random words, examine upper and lower bounds for the expected value of the longest common subsequences in this setting, and discuss the ...
  • On asymptotics of two non-uniform recursive tree models 
    Hiesmayr, Ella Veronika. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2017., 2017.)
    In this thesis the properties of two kinds of non-uniform random recursive trees are studied. In the first model weights are assigned to each node, thus altering the attachment probabilities. We will call these trees weighted ...
  • Self - adjoint extension theory of singular interactions 
    Türköz, Mustafa. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2017., 2017.)
    In this thesis, we study two-dimensional finite singular point interactions and three-dimensional finite singular interactions supported by curves on a compact Riemannian manifold. Our aim is to show that finite rank perturbations ...
  • Schubert varieties of Grassmannians 
    Altuğ, Kutsev Bengisu. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2017., 2017.)
    In this endeavor, studying Grassmannians in a ne and projective space is essential. We rstly present Grassmannians as varieties then divide Grassmannians into disjoint Schubert cells and apply Plucker embedding to realize ...
  • Different versions of the modularity theorem 
    Bildik, İlkiz. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2017., 2017.)
    One of the most interesting results in number theory is the proof of the Modu larity Theorem. The Modularity Theorem has many different versions. The geometric version states that there is a surjective morphism between ...
  • Homogeneous spacetime solutions of minimal massive gravity 
    Charyyev, Jumageldi. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2016., 2016.)
    In this thesis we rst study general mathematical properties of homogeneous spaces. We then review classi cation of three-dimensional Lie algebras, which was done by Bianchi. There are nine classes. In the last part we ...
  • Construction of surface bundles with non-zero signature 
    Köse, Feride Ceren. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2016., 2016.)
    In this thesis, we study a new method introduced by H. Endo, M. Korkmaz, D. Kotschick, B. Ozbagci, and A. Stipsicz in their paper [1] to construct surface bundles over a surface of genus 9 with signature 4.
  • Green biset functors and representation rings 
    Muslumov, Ruslan. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2017., 2017.)
    In this thesis, we investigate Green biset functors and clasi cation of sipmle modules over a Green biset functors in some special cases. Our aim is to see what conditions on the Green functor makes simple modules over it ...

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