The PhD defence will be partially digital, in room 720, 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.
Trial lecture
4th of March, 12:00, 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
To a mathematician, a surface is a shape that, upon close enough inspection, looks like a flat piece of paper around each of its points. Thus, to an ant, the surface of a bagel is conceived as flat, while the (roughly) spherical surface of the earth looks flat to us. Nevertheless, on a global level these shapes are topologically distinct in the sense that one cannot deform one into the other through stretching, bending and shrinking.
Manifolds generalize the notion of a surface to other dimensions. In this terminology, a surface is a 2-manifold and a curve is a 1-manifold. These low-dimensional shapes have been completely classified. Much progress has been made in dimension 3, but several serious questions still remain.
In my thesis, I have explored a recent version of an algebraic invariant known as instanton Floer homology associated with a restricted class of 3-manifolds. It is built from geometric data extracted from the solution spaces of the instanton equation -- a partial differential equation special to dimension 3 and 4. I have developed algebra needed to properly define this invariant and provided complete calculations
for the binary polyhedral spaces -- a family of 3-manifolds intimately linked with the platonic solids and their symmetries. I have also employed techniques from quiver theory to construct several hyper-Kähler bordisms between members of this family.
Adjudication committee
Professor Nikolai Saveliev, University of Miami
Professor Victor Pidstrygach, Georg-August-Universität Göttingen
Associate Professor Kris Shaw, University of Oslo
Supervisors
Associate Professor Kim Anders Frøyshov, University of Oslo
Professor John Rognes, University of Oslo
Chair of defence
Head of Department Geir Dahl, University of Oslo
Host of the session
Associate Professor Kris Shaw, University of Oslo