Hey! I'm Simon Halvdansson,

a PhD candidate in the analysis group at the Norwegian University of Science and Technology (NTNU) in Trondheim, Norway, studying under the supervision of Professor Franz Luef. My research is in time-frequency analysis using tools from harmonic analysis, functional analysis and operator theory. More specifically, much of my research is connected to the framework of quantum harmonic analysis.

Apart from my interest in mathematics, I have a background in physics, programming and deep learning, and currently maintain the open source Android Hacker News client Harmonic.

ArXiV GitHub LinkedIn

Publications

\(\boldsymbol{\mu \star S}\)
Measure-operator convolutions and applications to mixed-state Gabor multipliers
August 2023
with Hans Feichtinger and Franz Luef
ArXiV
\(\boldsymbol{f \star_G S}\)
Quantum harmonic analysis on locally compact groups
October 2022
Journal of Functional Analysis ArXiV
\(\boldsymbol{A_f^g \mapsto f}\)
Five ways to recover the symbol of a non-binary localization operator
January 2023
ArXiV
\(\boldsymbol{\operatorname{argmin}_f \mathcal{L}_{\mathrm{P}}(f)}\)
Existence of Uncertainty Minimizers for the Continuous Wavelet Transform
August 2021
with Jan-Fredrik Olsen, Ron Levie and Nir Sochen
Mathematische Nachrichten ArXiV

Talks/posters

International Workshop on Operator Theory and its Applications (IWOTA 2023)
July 31 - August 4, 2023
Helsinki, Finland
Workshop on quantum harmonic analysis (QHA2023)
June 5-9, 2023
NTNU Trondheim, Norway
Dynamics in the noncommutative world (DNCW 2023)
January 26, 2023
NTNU Trondheim, Norway
Oberseminar Analysis
October 4, 2022
Leibniz Universität Hannover, Germany
International Conference on Computational Harmonic Analysis (ICCHA 2022)
September 12-16, 2022
Ingolstadt, Germany
International Workshop on Operator Theory and its Applications (IWOTA 2022)
September 6-10, 2022
Krakow, Poland
Applied Harmonic Analysis and Friends (Strobl2022)
June 19-25, 2022
Strobl, Austria
Online International Conference on Computational Harmonic Analysis (ICCHA 2021)
September 13-17, 2021
Online

Projects

Harmonic for Hacker News
Harmonic is currently the most popular Hacker News client for Android with over 6000 daily active users and 60 000 downloads. As of summer 2023, it is open source and development is still ongoing. The focus of the app is on customizability, performance and a sleek modern design.
Play Store GitHub
Existence and Approximations of Optimal Wavelets
This is my master's thesis from Lund University, supervised by Jan-Fredrik Olsen and later on also Ron Levie. While relying heavily on earlier work by Ron Levie and Nir Sochen, we investigate an uncertainty functional measuring the localization of a wavelet. As it is a master thesis, there is a large focus on going over previous research and motivating the functional properly. In the end, we show that minimizers exists and can be approximated by considering minimizers on lower dimensional subspaces which can be constructed numerically.
Link PDF Minimizers
Computations with the 2D Coulomb Gas
My bachelor's thesis, also written at Lund University but with Yacin Ameur, is a thorough introduction to the 2D Coulomb gas and contains some (minor) novel results. The field has quite a deep background which is investigated and we motivate the construction of the main objects of the field. Moreover, there is also a simulation of these types of particle systems which can run with up to 50 000 particles on regular consumer hardware. Originally, the simulator could only handle 5000 particles but I rewrote it to utilize web worker multithreading in 2023.
PDF Simulator GitHub
Pay Back - IOU Manager
In high school I developed a series of Android apps and Pay Back, while quite outdated, is the only one which is still live on the Play Store. It was a joint project with John Rapp Farnes who focused more on the internals while I was responsible for design and UI, however our work often intersected. An IOU (I Owe yoU) manager keeps track of personal debts; this was from before you could painlessly send money to your friends. It has a ton of intricate features such as using NFC to sync your debts with friends which I guess is the highest form of feature creep.
Play Store