The PhD defence will be partially digital, in room 1259, Abels Utsikt - Niels Henrik Abels hus 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 request to access (available from 10th March 1:15 pm until 24th March 1:15 pm)
Trial lecture
24th of March, time: 10:15 am, room 1259 and Zoom.
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Join the trial lecture
The webinar opens for participation just before the trial lecture starts, participants who join early will be put in a waiting room.
Main research findings
Solving equations has always been one of the core areas of mathematics. One important class of equations are so-called polynomial equations. These appear naturally in a broad collection of fields, such as number theory, particle physics and optimization. Studying the solutions to such equations is the domain of the mathematical subfield called algebraic geometry.
When attempting to solve polynomial equations, one quickly notices that it is hard to give an explicit description of the solutions, a so-called parametrization. In fact, such a description is often outright impossible! But occasionally, one can find a clever trick that allows for a complete and explicit parametric description of the solutions. For any given polynomial equation, it is therefore natural to ask whether an explicit description is provably impossible, or if searching for a clever trick for describing the solution is warranted.
This thesis answers such questions by computing so-called birational invariants. These are computed for many types of polynomial equations where they were not previously known. By doing so, new examples of polynomial equations are found where the solutions cannot be described in an explicit, parametric form.
Adjudication committee
- Professor Ana-Maria Castravet, Université Paris-Saclay, Versailles
- Professor Hamid Abban, University of Nottingham
- Associate Professor Kim Frøyshov, University of Oslo
Supervisors
- Professor John Christian Ottem, University of Oslo
- Professor Kristian Ranestad, University of Oslo
- Associate Professor Jørgen Vold Rennemo, University of Oslo
Chair of defence
Head of Department Geir Dahl
Host of the session
Associate Professor Kim Frøyshov, University of Oslo