Recent Submissions

  • Monoid actions, their categorification and applications 

    Erdal, Mehmet Akif (Bilkent University, 2017-01)
    We study actions of monoids and monoidal categories, and their relations with (co)homology theories. We start by discussing actions of monoids via bi-actions. We show that there is a well-defined functorial reverse action ...
  • Deformation classes of singular quartic surfaces 

    Aktaş, Çisem Güneş (Bilkent University, 2017-01)
    We study complex spatial quartic surfaces with simple singularities and give their classication up to equisingular deformation. Simple quartics are K3-surfaces and as such they can be studied by means of the global Torelli ...
  • 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 ...
  • Numerical study of orthogonal polynomials for fractal measures 

    Şimşek, Ahmet Nihat (Bilkent University, 2016-07)
    In recent years, potential theory has an essential effect on approximation theory and orthogonal polynomials. Basic concepts of the modern theory of general orthogonal polynomials are described in terms of Potential Theory. ...
  • On some of the simple composition factors of the biset functor of P-permutation modules 

    Karagüzel, Çisil (Bilkent University, 2016-07)
    Let k be an algebraically closed field of characteristic p, which is a prime, and C denote the field of complex numbers. Given a finite group G, letting ppk(G) denote the Grothendieck group of p-permutation kG-modules, we ...
  • Geodesics of three-dimensional walker manifolds 

    Büyükbaş Çakar, Gökçen (Bilkent University, 2016-07)
    We review some basic facts of Lorentzian geometry including causality and geodesic completeness. We depict the properties of curves and planes in threedimensional Minkowski space. We deffne the Walker manifolds, that is, ...
  • Homotopy colimits and decompositions of function complexes 

    Çakar, Adnan Cihan (Bilkent University, 2016-07)
    Given a functor F : C→ GSp, the homotopy colimit hocolimCF is defined as the diagonal space of simplicial replacement of F. Let G be a finite group and F be a family of subgroups of G, the classifying space EFG can be taken ...
  • Groebner basis approach in graph-theoretical problems 

    Örün, Onur Muharrem (Bilkent University, 2016-06)
    In the study of graphs, it is often desirable to know about the colorability properties of a given graph or whether it is planar or if it contains a Hamiltonian cycle. We consider such problems and describe corresponding ...
  • On complete intersections and connectedness 

    Önal, Meltem (Bilkent University, 2002)
    In this thesis, we study the relation between connectedness and complete intersections. We describe the concept of connectedness in codimension k. We also study the basic facts about Cohen-Macaulay rings, and give ...
  • On the minimal number of elements generating an algebraic set 

    Şahin, Mesut (Bilkent University, 2002)
    In this thesis we present studies on the general problem of finding the minimal number of elements generating an algebraic set in n-space both set and ideal theoretically.
  • Concrete sheaves and continuous spaces 

    Özkan Recep (Bilkent University, 2015)
    In algebraic topology and differential geometry, most categories lack some good ”convenient” properties like being cartesian closed, having pullbacks, pushouts, limits, colimits... We will introduce the notion of continuous ...
  • Blocks of quotients of mackey algebras 

    Dar, Elif Doğan (Bilkent University, 2015)
    We review a theorem by Boltje and K¨ulshammer which states that under certain circumstances the endomorphism ring EndRG(RX) has only one block. We study the double Burnside ring, the Burnside ring and the transformations ...
  • Biset functors and brauer's induction theorem 

    Öğüt, İsmail Alperen (Bilkent University, 2014)
    We introduce two algebras on the endomorphism ring of the direct sum of character rings of groups from some collection. We prove the equality of these algebras to simplify a step in the proof of Brauer’s Induction Theorem. ...
  • Kuroda's class number formula 

    Şahinoğlu, Hatice (Bilkent University, 2007)
    In number theory theory, the class number of a field is a significant invariant. All over the time, people have come up with formulas for some cases and in this thesis I will discuss a proof of a class number formula for ...
  • Distance between a maximum point and the zero set of an entire function 

    Üreyen, Adem Ersin (Bilkent University, 2006)
    We obtain asymptotical bounds from below for the distance between a maximum modulus point and the zero set of an entire function. Known bounds (Macintyre, 1938) are more precise, but they are valid only for some maximum ...
  • Logarithmic dimension and bases in whitney spaces 

    Şengül, Yasemin (Bilkent University, 2006)
    In generalization of [3] we will give the formula for the logarithmic dimension of any Cantor-type set. We will demonstrate some applications of the logarithmic dimension in Potential Theory. We will construct a polynomial ...
  • Complete positivity in operator algebras 

    Kavruk, Ali Şamil (Bilkent University, 2006)
    In this thesis we survey positive and completely positive maps defined on operator systems. In Chapter 3 we study the properties of positive maps as well as construction of positive maps under certain conditions. In ...
  • Interpolating bases in the spaces of C(formula)-functions on cantor-type sets 

    Özfidan, Necip (Bilkent University, 2006)
    In this work by using the method of local interpolat ions suggested in [9] we construct topological bases in the spaces of CP-functions defined on uniformly perfect compact sets of Cantor type. Elements of the basis are ...
  • Applications of duality for Hp spaces 

    Yapıcı, Eser (Bilkent University, 2006)
  • Modular vector invariants 

    Madran, Uğur (Bilkent University, 2006)
    Vector invariants of finite groups (see the introduction for definitions) provides, in general, counterexamples for many properties of the invariant theory when the characteristic of the ground field divides the group ...

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