This thesis is concerned with rationality questions of algebraic varieties, specifically questions regarding stable rationality over the complex numbers. We use the techniques related to the motivic volume introduced by ...

\textit{Isogeny graphs} are a type of graphs, where the vertices represent elliptic curves and the edges represent isogenies. I will examine some of the structures of these graphs in this thesis. It turns out that the ...

The main aim of the thesis is to study attractors for certain iterated function systems arising from quantum channels on finite dimensional C*-algebras. I will show the existence of attractors on the density operators by ...

Fairness is an inherently important aspect of decision-making in general, and with automated algorithms increasingly making decisions impacting our lives it is of paramount importance that the decisions they make be fair ...

Statistical boosting is a powerful tool that has become increasingly more popular in recent years. It works very well in the high-dimensional data setting, and it has many beneficial properties, e.g., shrinkage, automated ...

Seifert manifolds play a crucial role in the classification of 3-manifolds, as they occupy six of the eight geometries proposed by Thurston. In this thesis we determine which Seifert manifolds can be given a smooth action ...

Denne oppgaven har som mål å drøfte ikke-standard analyse som et alternative til tradisjonell undervisning i kalkulus på videregående skole og begynnende universitet. For å kunne drøfte denne problemstillingen, vil oppgaven ...

In this thesis we reproduce the results of Laca and Neshveyev for characterizing certain KMS states on Pimsner algebras. Before getting there, we build up the necessary theory using various sources, giving detailed proofs ...

Certain polyhedral fans can be constructed from matroids, and these serve as the local model of tropical manifolds. Such matroidal fans satisfy a tropical version of Poincaré duality [JRS17]. In this thesis, we give ...

Vi ser på Schoof's og Satoh's algoritmer for opptelling av rasjonale punkter på elliptiske kurver over endelige kropper. Relevant bakgrunn om elliptiske kurver og de p-adiske tallene. Kort om ECC (elliptic curve cryptography). ...

Denne oppgaven tar for seg projeksjoner på vegger. Når man projiserer et bilde på en vegg, ønsker man at det ikke skal bli fordreid. Vi vil ta for oss hvordan punkter, linjer og flater blir projisert, og viser at avbildningene ...

Datamaskinen har i det siste århundret drastisk endret måten vi forholder oss til matematiske og naturvitenskapelige problemer, da en datamaskin har en beregningskapasitet som vi før bare kunne drømme om. Som en følge av ...

The purpose of this thesis is to look at certain abelian groups and their reduced twisted group C*-algebras. We consider a class of quantum channels on these algebras, associated with normalised positive definite functions, ...

This master thesis will demonstrate how to price perpetual American options with linear programming. American options are used both for hedging and speculation, and being able to price derivatives, without creating arbitrage ...

In this thesis we implement and employ a simplex spline basis developed by Cohen, Lyche, and Riesenfeld for the space of C1 quadratic splines on the Powell–Sabin 12-split of a triangle. A matrix recursion is used for ...

In this thesis, we consider the mod 2 homology of Q≥0S0 as an E∞ space and show the following. The homologies H*Q≥0S0 and H*C∞S0 are isomorphic as free commutative /2-algebras. The homology H*Q≥0S0 is generated as an ...

In this thesis we begin by looking at polynomials of m n x n matrices invariant under simultaneous conjugation. Thereafter we connect the invariant polynomials to simple representations of noncommutative plane curves, ...

A Heron triangle is a triangle with integer sides and integer area. A rational triangle is a triangle with rational sides and area. We will set out to prove van Luijks Theorem, that there exist infinitely many non-similar ...

The recent results on non-uniqueness of the Euler equations, all based on the theory developed in the papers by Camillo De Lellis and László Székelyhidi Jr., are believed to be connected to the theory of turbulent fluid ...

In this master thesis we will prove Dirichlet's theorem on primes in arithmetic progressions. The theorem states that there are an infinite number of primes in every primitive residue class modulo any positive number q, ...

Given a non-principal ultrafilter, we define and prove properties of ultralimits of measure spaces (including σ-algebras, filtrations and measures), random variables and discrete-time stochastic processes. Among other ...

This thesis investigates cubic hypersurfaces and their Fano schemes. After introducing the Fano schemes through low-dimensional examples, we move on to investigate cubic fourfolds. For the cubic fourfolds, we give complete ...

In this thesis we give an introduction to the Minimal Model Program and the Morrison-Kawamata cone conjecture. We then present some known results on anticanonical hypersurfaces building up to the result proven by Kollár ...

In this thesis we study the construction of wavelets for the Cuntz--Krieger $C^{\ast}$-algebras as developed by M. Marcolli and A. Paolucci in [MP11]. We identify and correct some errors in the construction, as well as ...

In this thesis, we study what can be said about Fermat's Last Theorem using only elementary methods. We will study the work of Sophie Germain and Niels Henrik Abel, both who worked with Fermat’s Last Theorem in the early ...

In this thesis we consider sextactic points on plane algebraic curves and a 2-Hessian curve that identifies these points. This curve was first established by Cayley, and we prove that Cayley's 2-Hessian is wrong. Moreover, ...

The main goal of this thesis is to reproduce the article [SW16] by Sims and Williams, categorising the primitive ideal space of the class of Deaconu- Renault groupoid C*-algebras generated by N_0^k-actions. We go through ...

Målet ved denne artikkelen er å analysere forholdet mellom vri- og flyttespill og symmetrigruppen. Vi skal se sammenhengen mellom gruppeteori og mange populære spill, spesielt når man vil løse spillene

We consider the bidomain model of cardiac electrophysiology. Departing from a discrete cellular model we derive the bidomain equations by homogenization. Using two-scale convergence we provide a rigorous homogenization ...

In this thesis we will study the phase space, Ph(A), for an associative k-algebra A. The phase space can be considered as a noncommutative tangent bundle. We will derive algebraic notions of points, curves, tangent vectors ...

In this thesis, we consider applications of directed algebraic topology in optimization theory, by representing directed graphs as directed topological spaces. We review the classical max-flow min-cut theorem and a ...

In their article, "Continuity of the Spectrum of a Field of Self-Adjoint Operators", Beckus and Bellissard discuss the following problem: Given a family of bounded, self-adjoint linear operators indexed by a parameter t ...

Parallellaksiomet er det eneste aksiomet der hyperbolsk geometri skiller seg fra euklidsk. Mens det i euklidsk geometri er en unik linje som går gjennom et gitt punkt og er parallell med en gitt linje, finnes det i hyperbolsk ...

Denne oppgaven er skrevet i faget MAT5930L, som er det siste faget i Lektorprogrammet ved UiO. Emnet er Euklids Elementer. Vi ser på noen av proposisjonene i de tre første bøkene av Elementer. Her fokuserer vi på hvordan ...

This thesis studies a relationship between solving optimal stopping problems and solving the weak variational inequalites. We prove a theorem that presents conditions under which the weak variatonal inequalities have a ...

Målet med denne masteroppgaven er å se på teorien som ligger til grunn for en rangeringsmodell kalt Offense-Defense Modellen. Jeg skriver om matriseskaleringer og dobbeltstokastiske matriser som ender med Sinkhorn-Knopp ...

The study of generic quartic symmetroids in projective 3-space dates back to Cayley, but little is known about the special specimens. This thesis sets out to survey the possibilities in the non-generic case. We prove that ...

This thesis aims to study the risk measure Conditional Value-at-Risk and analyse an optimization problem of maximizing expected return subject to this risk measure. The analysis include performing Fourier-Motzkin eliminations ...

Denne oppgaven studerer Reed-Solomon-koder og ser på hvordan dekoding av disse kan relateres til å finne potenssumdekomposisjoner av polynomer, hvilket kan tolkes geometrisk som å finne et sekantplan til den rasjonale ...

En polytop er et legeme i det euklidske rom som avgrenses av et endelig antall hyperplan. Vi kan legge på ulike begrensninger på polytopene og få et ulikt utvalg polytoper. I denne avhandlingen ser vi på polytoper av ulik ...

A detailed study of computable iterations of Gödel-sentences, both in normal recursion and generalisations to other recursive theories.

In 1862, substituting for professor O. J. Broch, Ludvig Sylow gives the first lectures ever given on the field of Galois theory in Norway, at the University of Christiania. He lectures on, amongst other things, what he ...

Punktene på en elliptisk kurve danner en gruppe. Hvis vi kaller origo i gruppa for Q, er et n-torsjonspunkt et punkt P som er slik at nP=Q. Mengden n-torsjonspunkter danner en abelsk gruppe. Alle 3-torsjonspunktene på en ...

An examination of the abridged notation introduced by Salmon for plane geometry. Culminating in its use to prove the theorems of Brianchon and Pascal, Steiner's theorem on Pascal's Hexagon and Steiner's solution of the ...

The first part of the thesis concerns the problem of ranking in general. We take a closer look at the two ranking methods; Elo rating and Colley rating. The former is used to rate and rank chess players, whereas the latter ...

One of the puzzlingly hard problems in \emph{Computer Aided Geometric Design} and \emph{Approximation Theory} is that of finding the dimension of the spline space of $C^r$ piecewise polynomials of degree $n$ over a planar ...

In elliptic curve cryptography, the choice of the elliptic curve is important for security. This is because there exist elliptic curves where certain shortcuts can be made that breaks the security of elliptic curve ...

In this thesis we compute the K_2-homology of B^3\Z=K(\Z,3) following Ravenel-Wilson, and exhibit all ring spectrum maps from \Sigma^\infty B^3\Z_+ to K_2. We define the complex oriented theory K_n as a quotient of Lubin-Tate ...

The thesis solves the problem of finding the local-risk minimizing strategies in an incomplete market of electricity and fuels where there is a time-change. This is done under two methodologies: in the classical sense and ...

In this thesis we will consider Markov operators on cones . More precisely, we let X equipped with certain norm be a real Banach space, K in X be a closed, normal cone with nonempty interior, e in Int (K) be an order unit. ...

We define various notions of rank of a polynomial, and study them via apolarity. We treat the notion of natural rank in particular depth, and classify ternary forms of degree at most four and quaternary forms of degree at ...

In 1968 John Milnor published his now classic "Singular points of complex hypersurfaces". In this he proved the following theorem: Let f be a holomorphic function from n-dimensional complex space to one-dimensional complex ...

By a result due to F. Forstnerič, injective holomorphic maps defined and close to the identity on a certain neighborhood of the intersection of A and B (where (A,B) is a Cartan pair in a complex manifold X) admit compositional ...

In this thesis we study a class of irreversible, stochastic investment models where the optimal strategy can be computed exactly. The optimal strategy is always to invest just enough to keep the investment process outside ...

In this master’s thesis we define a pricing model for futures contracts by using Lévy processes in an infinite dimensional Hilbert space H. The elements in H are assumed to be absolutely continuous functions on the positive ...