The PhD defence will be in Abels utsikt - Niels Henrik Abels hus. 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.
Trial lecture
October 6th, time: 10:15 am, room 1259 (Abels utsikt).
Prismatic cohomology and topological Hochschild homology
Main research findings
Motivic homotopy theory, developed by Morel and Voevodsky in the 1990s, transfers ideas from algebraic topology to algebraic geometry and led to landmark results such as Voevodsky’s proofs of the Milnor and Bloch–Kato conjectures.
Classical motivic homotopy theory identifies two objects if they can be connected via the affine line. While effective in many cases, it does not capture important phenomena arising from singularities or degenerations. Logarithmic geometry, introduced by Kato, Fontaine, and Illusie, provides a natural framework to study these subtler situations. Building on this, Binda, Park, and Østvær developed logarithmic motivic homotopy theory, replacing the affine line with its logarithmic compactification.
Within this context, my work provides two new descriptions of logarithmic motivic spectra, equipping them with improved categorical properties. I also develop logarithmic versions of the h- and v-topologies for logarithmic schemes and prove that the log étale cohomology satisfies descent. This allows motivic methods to be applied to the étale topology with torsion coefficients in positive characteristic and suggests a method for defining logarithmic motives over log points.
Adjudication committee
- Professor Andreas Langer, University of Exeter
- Professor Katharina Hübner, Goethe University Frankfurt
- Professor Jørgen Vold Rennemo, University of Oslo
Supervisors
- Professor Paul Arne Østvær, University of Oslo
- Professor Tom Bachmann, University of Mainz
- Professor Frederico Binda, University of Milan
- Dr. Doosung Park, University of Wuppertal
Chair of defence
Head of Department Geir Dahl
Host of the session
Professor Jørgen Vold Rennemo, University of Oslo