Dept. of Mathematics  Ph.D. / Sc.D.
Recent Submissions

A conjecture on squarezero upper triangular matrices and Carlsson's rank conjecture
(Bilkent University, 201809)A wellknown conjecture states that if an elementary abelian pgroup acts freely on a product of spheres, then the rank of the group is at most the number of spheres in the product. Carlsson gives an algebraic version ... 
Dilations of doubly invariant kernels valued in topologically ordered * spaces
(Bilkent University, 201807)An ordered *space Z is a complex vector space with a conjugate linear involution *, and a strict cone Z+ consisting of self adjoint elements. A topologically ordered *space is an ordered *space with a locally convex ... 
Codes on fibre products of ArtinSchreier and Kummer coverings of the projective line
(Bilkent University, 200208)In this thesis, we study smooth projective absolutely irreducible curves defined over finite fields by fibre products of ArtinSchreier and Kummer coverings of the projective line. We construct some curves with many rational ... 
Asymptotics of extremal polynomials for some special cases
(Bilkent University, 201705)We study the asymptotics of orthogonal and Chebyshev polynomials on fractals. We consider generalized Julia sets in the sense of Br uckB uger and weakly equilibrium Cantor sets which was introduced in [62]. We give ... 
Extension problem and bases for spaces of infinitely differentiable functions
(Bilkent University, 201704)We examine the Mityagin problem: how to characterize the extension property in geometric terms. We start with three methods of extension for the spaces of Whitney functions. One of the methods was suggested by B. S. Mityagin: ... 
Monoid actions, their categorification and applications
(Bilkent University, 201701)We study actions of monoids and monoidal categories, and their relations with (co)homology theories. We start by discussing actions of monoids via biactions. We show that there is a welldefined functorial reverse action ... 
Deformation classes of singular quartic surfaces
(Bilkent University, 201701)We study complex spatial quartic surfaces with simple singularities and give their classication up to equisingular deformation. Simple quartics are K3surfaces and as such they can be studied by means of the global Torelli ... 
Concrete sheaves and continuous spaces
(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 ... 
Distance between a maximum point and the zero set of an entire function
(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 ... 
Modular vector invariants
(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 ... 
Extension operators for spaces of infinitely differentiable functions
(Bilkent University, 2005)We start with a review of known linear continuous extension operators for the spaces of Whitney functions. The most general approach belongs to PawÃlucki and Ple´sniak. Their operator is continuous provided that the ... 
Representations of functions harmonic in the upper halfplane and their applications
(Bilkent University, 2003)In this thesis, new conditions for the validity of a generalized Poisson representation for a function harmonic in the upper halfplane have been found. These conditions differ from known ones by weaker growth restrictions ... 
Code construction on modular curves
(Bilkent University, 2003)In this thesis, we have introduced two approaches on code construction on modular curves and stated the problems step by step. Moreover, we have given solutions of some problems in road map of code construction. One of ... 
Recursion operator and dispersionless Lax representation
(Bilkent University, 2002)We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a dispersionless Lax representation. We consider a polynomial and rational Lax function. We give several ... 
Piatetskishapir prime number theorem and chebotarev density theorem
(Bilkent University, 201507)Let K be a nite Galois extension of the eld Q of rational numbers. In this thesis, we derive an asymptotic formula for the number of the PiatetskiShapiro primes not exceeding a given quantity for which the associated ... 
Essays in collective decision making
(Bilkent University, 201410)Four different problems in collective decision making are studied, all of which are either formulated directly in a gametheoretical context or are concerned with neighboring research areas. The rst two problems fall ... 
Painleve test and the Painleve equations hierarchies
(Bilkent University, 2001)Recently there has been a considerable interest in obtaining higher order ordinary differential equations having the Painleve property. In this thesis, starting from the first, the second and the third Painleve transcendents ... 
Gibbs measures and phase transitions in onedimensional models
(Bilkent University, 2000)In this thesis we study the problem of limit Gibbs measures in onedimensional models. VVe investigate uniqueness conditions for the limit Gibbs measures for onedimensional models. VVe construct a onedimensional model ... 
The solvability of PVI equation and secondorder seconddegree Painleve type equations
(Bilkent University, 1998)A rigorous method was introduced by Fokas and Zhou for studying the RiernaiinHilhert problem associated with the Painleve II and IV. The same methodology has been applied to Painleve I, III and V. In this thesis, we ... 
KOrings and Jgroups of lens spaces
(Bilkent University, 1998)In this thesis, we make the explicit computation of the real A'theory of lens spaces and making use of these results and Adams conjecture, we describe their .7groups in terms of generators and relations. These computations ...