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.
Join webinar.
Ex auditorio questions: the chair of the defence will invite the audience to ask questions ex auditorio at the end of the defence.
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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
February 20th, time: 10:15 am, room 1259 (Abels utsikt).
The Milnor conjecture in algebraic K-theory
Main research findings
In 1974, a landmark paper was published by Segal where he gave an elegant proof of the recognition principle, which states that the category of group like commutative monoids in spaces is equivalent to the category of connective spectra. Hence, spectra we know and love like ordinary cohomology HZ, connective complex and real K-theory ku and ko, cobordism MU and MO, and the sphere spectrum S, can be interpreted as spaces with additional group structure.
In the beginning of this millenium, the foundations for the algebro-geometric analog of this theory was sketched by Voevodsky, and later devloped by several others until very recently. Thus connective motivic spectra are given descriptions in terms of motivic spaces with some addtional group structure.
In this thesis, the hyperétale version of this theory is established, which means replacing the Nisnevich topology from the motivic theory with the hypercomplete étale topology. This yields a similar dictionary as above between connective hyperétale motivic spectra and hyperétale motivic spaces with some additional group structure. As applications we prove the the hyperétale localization functor commutes with the infinite G_m-loop functor, and that a certain Betti realization coincides with taking global sections.
Adjudication committee
- Professor Alexander Vishik, University of Nottingham
- Lecturer Glen Wilson, Universitetet i Tromsø
- Associate Professor Kim Anders Frøyshov, University of Oslo
Supervisors
- Professor Paul Arne Østvær, University of Oslo
- Researcher Elmanto Elden, Harvard University
- Professor Tom Bachmann, Johannes Gutenberg University Mainz
- Professor John Christian Ottem, University of Oslo
Chair of defence
Head of Department Erlend Fornæss Wold.
Host of the session
Associate Professor Kim Anders Frøyshov, University of Oslo