• Projective characters of finite groups 

  Yılmaz, Said. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)

  The purpose of this thesis to analyze the basic facts about projective characters of finite groups and compare them to the facts about ordinary characters of finite groups. We start with review of basic facts about the ...
• Kadison-Singer problem from a banach algebra perspective 

  Keçkin, Murat. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)

  In 1959, Kadison and Singer asked whether every pure state of the diagonal subspace D(ℓ2) of B(ℓ2) has a unique pure state extension to B(ℓ2). This problem has remained open until 2013; in 2013 it has been solved by a team ...
• Theory of noncommutative motives 

  Üze, Berkan. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)

  The theory of motives was originally conceived by Alexander Grothendieck as a universal cohomology theory for algebraic varieties. In the decades since it was first introduced, it has become a vast and profoundly sophisticated ...
• Monogenic number fields 

  Değirmenci, Pınar. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)

  Determining whether the ring of integers OK of an algebraic number field K of degree n admits a power integral basis is one of the classic problems in algebraic number theory. In other words, we want to determine whether ...
• On the hypersurfaces in toric varieties 

  Barış, İlayda. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)

  Theory of toric varieties provides fruitful interactions between algebraic geom etry and combinatorics. It is remarkably fertile in terms of connections with many areas of mathematics and has plentiful applications to other ...
• The question of model companionability : positive and negative answers 

  Berksoy, Feyza Nur. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)

  Model companion ofa universal theory T is the axiomatization of the existentially closed models of T. This thesis studies the concept of model companionability of theories. We present examples of model companions of certain ...
• Global well-posedness of NLS equations 

  Yılmaz, Oğuz. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)

  The thesis is a survey of the I-method. After introducing the method, we discuss the implementation of this method to cubic, defocusing nonlinear Schrödinger equation in the spatial dimension n = 2 and quintic, defocusing ...
• Covariance estimation of spatio-temporal random variables with kronecker product based models 

  Dağıdır, Can Hakan. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)

  Covariance estimation is a widely studied topic. Due to the nature of many prob lems, high-dimensional Spatio-temporal scenarios are considered frequently. In some cases, the true covariance matrices are also expected to ...
• Negative dependence in discrete probability :|notions, models and consequences 

  Çiçeksiz, Recep Altar. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2021., 2021.)

  In this thesis we study the negative dependence properties of random cluster measure. First, we introduce the notions of negative correlation and how they relate to each other. We observe that this important notion is ...
• 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. ...

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