The University of Oslo is closed. The PhD defence and trial lecture will therefore be fully digital and streamed directly using Zoom. The host of the session will moderate the technicalities while the chair of the defence will moderate the disputation.
Ex auditorio questions: the chair of the defence will invite the audience to ask questions ex auditorio at the end of the defence. If you would like to ask a question, click 'Raise hand' and wait to be unmuted.
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Join the disputation
The webinar opens for participation just before the disputation starts, participants who join early will be put in a waiting room.-
Submit the request to get access to the thesis (available from 9th June 13:15 until 23th June 13:15)
Trial lecture
"Multigrid methods"
Main research findings
Complex interactions between billions of nerve cells control our thoughts, emotions and behavior. Nerve cells communicate via electrical signals generated by molecules and ions moving over and between brain cells. In her dissertation, Ellingsrud, together with colleagues, has developed mathematical and numerical models for interactions between electrical and chemical processes in the brain. The models can potentially contribute to new insights in brain processes associted with altered ion concentrations.
Traditionally, ion concentrations between cells have been considered more or less constant during normal brain activity. Recent research efforts, however, show that these concentrations are not static, but change across brain states (e.g. sleep). Further, breakdown of ionic homeostasis in the brain is associated with pathologies such as migraine and epilepsy.
Mathematical models describing the interaction between ions and electrical activity typically consist of non-linear and coupled partial and ordinary differential equations that are challenging to solve numerically. Ellingsrud has considered two such models. In the first model, the cells are represented as a continuum, and is suitable for looking at waves of hyperactivity in epilepsy and migraine. The second model is more detailed and represents the cells explicitly, and is well suited for looking at local phenomena.