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Now showing items 1-10 of 51

#### The pandemic fusion system for endomorphism algebras of p-permutation modules

(Bilkent University, 2018-09)

During the 1980's Puig developed a new approach to modular representation
theory, introducing new p-local invariants and thereby extending Green's work on
G-algebras. We investigate the Puig category, commenting on its ...

#### Oscillation properties of stopped random walks on infinite tress

(Bilkent University, 2014)

We investigate a random walk on a branching tree with vertices labeled 1; 2; : : : ; r
which terminates if two consecutive vertices of a walk are labeled with close
numbers. It is proved that expected absorption times ...

#### Smoothness properties of Green's functions

(Bilkent University, 2014)

Basic notions of potential theory are explained with illustrative examples.
Many important properties, including the characteristic ones, of Green’s functions
that are defined by the help of equilibrium measures are ...

#### 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.

#### Characteristic bisets and local fusion subsystems

(Bilkent University, 2018-09)

Fusion systems are categories that contain the p-local 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 ...

#### On some of the simple composition factors of the biset functor of P-permutation modules

(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 ...

#### Groebner basis approach in graph-theoretical problems

(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 ...

#### Homotopy colimits and decompositions of function complexes

(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 ...

#### Smoothness of the green function for some special compact sets

(Bilkent University, 2010)

Smoothness of the Green functions for some special compact sets, which are
sequences of closed intervals with certain parameters, is described in terms of the
function ϕ(δ) = 1
log 1
δ
that gives the logarithmic measure ...

#### On the Nẹ́ron-severi lattice of Delsarte surfaces

(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 ...