Matematik: Recent submissions

  • Stationary distributions and convergence rates for the edge flipping process 
    Demirci, Yunus Emre. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2021., 2021.)
    The edge flipping process is a random walk over the set of all possible color patterns of a graph. Each time the two endpoints of the selected edge are colored the same color. This color is blue with probability p and red ...
  • Langlands reciprocity principle for GL(n) 
    Barbaros, Bahri Fatih. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2021., 2021.)
    Langlands program is one of the most significant areas of research in modern mathematics as it asserts a connection between number theory, representation the ory and automorphic forms. Langlands program is basically a study ...
  • Supersymmetric non-linear sigma models in D=2+1 dimensional spacetime 
    Bardavid, Metin. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2021., 2021.)
    In this thesis we study the theory of Supersymmetric Non-Linear a-Models. We first review the free scalar field theory which can be considered as a Linear a-model. We then discuss the Non-Linear a-model as well as the ...
  • Relative endo-trivial modules 
    Budak, Doğa Ulaş. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2021., 2021.)
    We first develop the necessary tools from the theory of G-algebras and endomorphism rings. Then the basic results of Green's theory of vertices and sources for kG-modules is given. Building on these, we retrace the steps ...
  • Asymptotically anti-de Sitter spacetimes in three dimensions 
    Deral, Ceren Ayşe. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2021., 2021.)
    In this thesis, we reviewed several aspects of asymptotically anti-de Sitter (AAdS) spacetimes in three dimensional Einstein gravity by following some important historical work. Starting with a brief introduction to anti-de ...
  • On online and approximate cover time problems 
    Yıldız, Mehmet Akif. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2020., 2020.)
    As a generalization of the classical coupon collector problem in the probability theory, the cover time in random walks on Markov chains has been investigated in numerous studies in the literature. Especially, there are ...
  • Variational methods for nonlinear elliptic partial differential equations with nonlocal terms 
    Topaloğlu, İhsan Ata. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2007., 2007.)
    In this thesis, existence of standing waves for the DaveyStewartson (DS) and generalized DaveyStewartson (GDS) systems are established using variational methods. Since both the DS system and the GDS system reduce to a ...
  • Central-firing of type A2n with initial weight 0 
    Cin, Uğur. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2020., 2020.)
    In this thesis a variant of the chip- ring game introduced by Hopkins, McConville and Propp in [1], called the labeled chip- ring on Z, is studied. We will rst explore the basic properties and examples of this game. We ...
  • Algebraic overtwised contact structures on 3-sphere 
    Karadereli, Şeyma. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2020., 2020.)
    It is known that all of the complex analytic singularity links and the associated Milnor open books on the 3-sphere correspond to a single contact structure, which is the unique tight structure of the 3-sphere. The main ...
  • Complex representations of finite general linear groups 
    Küçük, Ebru Beyza. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.)
    In this thesis, we determine complex irreducible representations of GL(2,K), the group of 2 by 2 invertible matrices over a finite field K. Actually, this is done by Ilya Piatetski-Shapiro in 1983. In his article [1], Shapiro ...
  • ABC conjecture and its implications 
    Koç, Tuğçe. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.)
    In this thesis, our aim is to state the importance of abc conjecture and prove the strong results we obtain with the help of abc conjecture. First, we give necessary notions and tools which are used throughout the thesis. ...
  • 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 ...

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