Browsing Dept. of Mathematics  Master's degree by Title
Now showing items 1130 of 119

Canonical induction for trivial source rings
(Bilkent University, 2013)We discuss the canonical induction formula for some special Mackey functors by following the construction of Boltje. These functors are the ordinary and modular character rings and the trivial source rings. Making use ... 
Chain maps between Gruenberg resolutions
(Bilkent University, 201808)Let G be a finite group. For a given presentation of G = hFRi, Gruenberg gives a construction of a projective resolution for Z as a ZGmodule. This resolution, which is called Gruenberg resolution, only depends on the ... 
Characteristic bisets and local fusion subsystems
(Bilkent University, 201809)Fusion systems are categories that contain the plocal 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 ... 
Classical Zariski pairs with nodes
(Bilkent University, 2008)In this thesis we study complex projective sextic curves with simple singularities. All curves constituting classical Zariski pairs, especially those with nodes, are enumerated and classified up to equisingular deformation. ... 
Cobordism calculations with Adams and James spectral sequences
(Bilkent University, 2010)Let ξn : Z/p → U(n) be an ndimensional faithful complex representation of Z/p and in : U(n)→O(2n) be inclusion for n ≥ 1. Then the compositions in ◦ ξn and jn ◦ in ◦ ξn induce fibrations on BZ/p where jn : O(2n) → O(2n ... 
Cohomological dimension and cubic surfaces
(Bilkent University, 2004)In this thesis we give necessary and sufficient conditions for a curve C on a given cubic surface Q so that Q − C is affine. We use this to give a simpler proof of cd(P 3 − C) = 1 by using Budach’s method for these ... 
Cohomology of semidirect products
(Bilkent University, 2012) 
Complete positivity in operator algebras
(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 ... 
Conditions for uniqueness of limit Gibbs states
(Bilkent University, 1998)In this work we studied the problem of phase transitions in onedirnensional models with unique ground state. A model ha\dng two spins, one ground state and exhibiting phase transition is constructed. 
Consistency in house allocation problems
(Bilkent University, 1999) 
Construction of modular forms with Poincaré series
(Bilkent University, 2010)In this thesis, we construct holomorphic modular forms of integral weight k > 2 for the principle congruence subgroup Γ( ¯ N) by means of Poincar´e series. We start by providing the necessary background information on ... 
Critical probabilities of percolation on graphs and random trees
(Bilkent University, 2014)We consider the model of independent percolation on various graphs and random trees. We investigate the critical probabilities of bond and site percolation on these graphs. 
Curves in projective space
(Bilkent University, 2003)This thesis is mainly concerned with classification of nonsingular projective space curves with an emphasis on the degreegenus pairs. In the first chapter, we present basic notions together with a very general notion ... 
Dilation theorems for VHspaces
(Bilkent University, 2009)In the Appendix of the book Le¸cons d’analyse fonctionnelle by F. Riesz and B. Sz.Nagy, B. Sz.Nagy [15] proved an important theorem on operator valued positive definite maps on ∗semigroups, which today can be considered ... 
The distance between maximum modulus points and the zero set of an entire function
(Bilkent University, 2001) 
Existence of basis in some Whitney spaces
(Bilkent University, 2003)Existence of basis in locally convex spaces has been a hot subject in functional analysis for more than 40 years. We will give some partial solutions to this wellknown problem. We will demonstrate two cases of Cantortype ... 
Explicit reciprocity laws
(Bilkent University, 2010)Quadratic reciprocity law was conjectured by Euler and Legendre, and proved by Gauss. Gauss made first generalizations of this relation to higher fields and derived cubic and biquadratic reciprocity laws. Eisenstein and ... 
The extension class of a subset complex
(Bilkent University, 2006) 
Extremal problems and bergman projections
(Bilkent University, 201707)Studying extremal problems on Bergman spaces is rather new and techniques used are usually specific to the problem to be solved. However, a 2014 paper by T. Ferguson developed a systematic method using Bergman projections ... 
Extreme behavior of lex ideals on Betti numbers
(Bilkent University, 2013)This paper mainly deals with the finitely generated graded modules of the polynomial ring k[x1, x2, ..., xn]. Free resolutions is an important tool to understand the structure of these modules. Betti numbers are an useful ...