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Discovering Best Practices for Educational Video Conferencing Systems
(Chapter, 2023)Digitalization of higher education is amongst the most important and most researched areas in recent years. The COVID19 pandemic ensured rapid movement into less known environments of the digitization process, online ... -
Verifiable Mix-Nets and Distributed Decryption for Voting from Lattice-Based Assumptions
(Journal article; Peer reviewed, 2023)Cryptographic voting protocols have recently seen much interest from practitioners due to their (planned) use in countries such as Estonia, Switzerland, France, and Australia. Practical protocols usually rely on tested ... -
Security Model for Privacy-Preserving Blockchain-Based Cryptocurrency Systems
(Lecture Notes in Computer Science;13983, Chapter, 2023)Privacy-preserving blockchain-based cryptocurrency systems have become quite popular as a way to provide confidential payments. These cryptocurrency systems differ in their designs, underlying cryptography, and confidentiality ... -
Picard's little theorem
(Bachelor thesis, 2024)Denne oppgaven gir et bevis av Picard's lille teorem ved å bruke en modulær funksjon, analytisk fortsettelse og Liouville's teorem. Etter noen nødvendige forberedelser, starter vi konstruksjonen av den modulære funksjonen ... -
Hybrid Group Key Exchange with Application to Constrained Networks
(Peer reviewed; Journal article, 2023)We expand the security model for group key exchange of Poettering et al. (CT-RSA 2021) to allow for more fine-tuned reveal of both state and keying material. The expanded model is used to analyse the security of hybrid ... -
A Lipschitz metric for ⍺-dissipative solutions to the Hunter-Saxton equation
(Journal article; Peer reviewed, 2024)We explore the Lipschitz stability of solutions to the Hunter–Saxton equation with respect to the initial data. In particular, we study the stability of α-dissipative solutions constructed using a generalised method of ... -
Solitary waves for dispersive equations with Coifman–Meyer nonlinearities
(Journal article; Peer reviewed, 2024)Using a modified version of Weinstein’s argument for constrained minimization in nonlinear dispersive equations, we prove existence of solitary waves in fully nonlocally nonlinear equations, as long as the linear multiplier ... -
REMARKS ON SOLITARY WAVES IN EQUATIONS WITH NONLOCAL CUBIC TERMS
(Journal article; Peer reviewed, 2024)In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form ∂tu +∂x(Λsu+uΛru2) = 0, where Λs,Λr are Bessel-type Fourier multipliers. The linear ... -
B-series for SDEs with application to exponential integrators for non-autonomous semi-linear problems
(Journal article; Peer reviewed, 2024)In this paper a set of previous general results for the development of B–series for a broad class of stochastic differential equations has been col- lected. The applicability of these results is demonstrated by the derivation ... -
Key Exchange in Special Circumstances
(Doctoral theses at NTNU;2024:246, Doctoral thesis, 2024) -
Poissonian correlations of higher orders
(Peer reviewed; Journal article, 2023) -
A note on Real line bundles with connection and Real smooth Deligne cohomology
(Peer reviewed; Journal article, 2024)We define a Real version of smooth Deligne cohomology for manifolds with involution which interpolates between equivariant sheaf cohomology and smooth imaginary-valued forms. Our main result is a classification of Real ... -
Internal Higher Category Theory
(Doctoral theses at NTNU;2024:251, Doctoral thesis, 2024)The goal of this thesis is to lay the foundations for a theory of ∞-categories internal to an ∞-topos B. Our model for such internal ∞-categories is based on the notion of a complete Segal object, but can equivalently be ... -
Spectral Invariance of ∗ -Representations of Twisted Convolution Algebras with Applications in Gabor Analysis
(Journal article; Peer reviewed, 2021)We show spectral invariance for faithful ∗-representations for a class of twisted convolution algebras. More precisely, if G is a locally compact group with a continuous 2-cocycle c for which the corresponding Mackey group ... -
Cohomologies of complex manifolds with symplectic (1, 1)-forms
(Journal article; Peer reviewed, 2023)Let (X,J) be a complex manifold with a non-degenerated smooth d-closed (1,1)-form ω. Then we have a natural double complex ∂ +∂Λ, where ∂Λ denotes the symplectic adjoint of the ∂-operator. Westudy the Hard Lefschetz Condition ... -
Curvature of the base manifold of a Monge–Ampère fibration and its existence
(Journal article; Peer reviewed, 2022)In this paper, we consider a special relative Kähler fibration that satisfies a homogenous Monge–Ampère equation, which is called a Monge–Ampère fibration. There exist two canonical types of generalized Weil–Petersson ... -
Metric results on summatory arithmetic functions on Beatty sets
(Peer reviewed; Journal article, 2021) -
On a remark by Ohsawa related to the Berndtsson-Lempert method for L2-holomorphic extension
(Journal article; Peer reviewed, 2022)In [15, Remark 4.1], Ohsawa asked whether it is possible to prove Theorem 4.1 and Theorem 0.1 in [15] using the Berndtsson–Lempert method. We shall answer Ohsawa’s question affirmatively in this paper. Our approach also ... -
Distributional Generating Series in Nonlinear Control Theory
(Chapter, 2024)In linear system theory, the commutative algebra of integrable functions under convolution does not have a unit unless one includes the Dirac delta or impulse function. In the broader context of nonlinear systems, such ... -
Quipu Quivers and Nakayama Algebras with Almost Separate Relations
(Journal article; Peer reviewed, 2023)A Nakayama algebra with almost separate relations is one where the overlap between any pair of relations is at most one arrow. In this paper we give a derived equivalence between such Nakayama algebras and path algebras ...
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