Theses  Department of Mathematics
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Haar systems on locally compact groupoids
(Bilkent University, 202207)Haar systems are generalizations of Haar measures on groups to groupoids. Naturally, important research directions in the field try to generalize the well known existence of a Haar measure on a locally compact group to the ... 
Extremal problems on Bergman spaces A¹α and Besov spaces
(Bilkent University, 202205)Extremal problems in different function spaces have long been investigated. Ferguson provides a method, using Bergman projections, to solve certain types of extremal problems in Bergman spaces for 1 < p < ∞ in his work ... 
Finite psubgroups of Sp(n)
(Bilkent University, 202109)Hikari [1] classiﬁes all ﬁnite psubgroups of simple algebras, and Banieqbal [2] classiﬁes the ﬁnite subgroups of 2×2 matrices over a division algebra of characteristic zero. In this thesis, we give a new proof for the ... 
Alexander modules of trigonal curves
(Bilkent University, 202101)We classify the monodromy Alexander modules of nonisotrivial trigonal curves. 
The geometry of sheaves on sites
(Bilkent University, 202101)In this work, we study doing geometry on sheaves on sites. Categories of our sites consist of objects that are building blocks for a given geometry. Generalized spaces then will be sheaves on these sort of sites. Next we ... 
Lebesgue constants on cantor type sets
(Bilkent University, 202009)The properties of compact subsets of the real line which are in the class of Bounded Lebesgue Constants (BLC) are investigated. Knowing that any such set must have 1dimensional Lebesgue measure zero and nowhere density, ... 
Deformations of some bisettheoretic categories
(Bilkent University, 202009)We define the subgroup category, a category on the class of finite groups where the morphisms are given by the subgroups of the direct products and the composition is the star product. We also introduce some of its ... 
Constructions and simplicity of the Mathieu groups
(Bilkent University, 202008)Of the 26 sporadic finite simple groups, 5 were discovered by E. Mathieu in 1861 and 1873 [1], [2]. These Mathieu groups are the focus of this thesis, where we will prove their simplicity using elementary methods. E. ... 
Mackey decomposition for Brauer pairs
(Bilkent University, 202008)For a ﬁnite group G and an algebraically closed ﬁeld k of characteristic p, a kalgebra A with a Gaction is called a Galgebra. A pair (P,c) such that P is a psubgroup of G and c is a block idempotent of the Galgebra ... 
Analysis on selfsimilar sets
(Bilkent University, 202008)Selfsimilar sets are one class of fractals that are invariant under geometric similarities. In this thesis, we study on selfsimilar sets. We give the deﬁnition of a selfsimilar set K and present the proof the existence ... 
Generic initial ideals of modular polynomial invariants
(Bilkent University, 202007)We study the generic initial ideals (gin) of certain ideals that arise in modular invariant theory. For all the cases where an explicit generating set is known, we calculate the generic initial ideal of the Hilbert ideal ... 
Effect of time delays on the convergence speed of consensus dynamics
(Bilkent University, 202001)We discuss consensus problems under time delays. The presence of time delays results in an inﬁnitedimensional system rather than a system of ordinary differential equations. It has been shown that information transmission ... 
Cohomology of infinite groups realizing fusion systems
(Bilkent University, 201909)Given a fusion system F defined on a pgroup S, there exist infinite group models, constructed by Leary and Stancu, and Robinson, that realize F. We study these models when F is a fusion system of a finite group G. If ... 
Canonical induction, Green functors, lefschetz invariant of monomial Gposets
(Bilkent University, 201906)Green functors are a kind of group functor, rather like Mackey functors, but with a further multiplicative structure. They are defined on a category whose objects are finite groups and whose morphisms are generated by ... 
Which algebraic K3 surfaces doubly cover an enriques surface: a computational approach
(Bilkent University, 201902)The relationship between K3 Surfaces and Enriques Surfaces is known to mathematicians for the last 30 years. We examined this relationship from a lattice theoretical point of view by looking at transcendental lattice of ... 
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 ... 
Which algebraic K3 surfaces cover an enriques surface
(Bilkent University, 201809)We partially determine the necessary and su cient conditions on the entries of the intersection matrix of the transcendental lattice of algebraic K3 surface with Picard number 18 (X) 19 for the surface to doubly ... 
The pandemic fusion system for endomorphism algebras of ppermutation modules
(Bilkent University, 201809)During the 1980's Puig developed a new approach to modular representation theory, introducing new plocal invariants and thereby extending Green's work on Galgebras. We investigate the Puig category, commenting on its ... 
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 ... 
Chain maps between Gruenberg resolutions
(Bilkent University, 201807)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 ...