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.
- Submit request to access (available from 22nd of February 1:15 pm until 7th of March 1:15 pm)
Trial lecture
7th of March, time: 10:15 am, room 1259 (Abels utsikt).
Torelli theorems
Main research findings
Since the early 2000s, tropical geometry has emerged as a field connecting combinatorics and algebraic geometry in novel ways. Matroids are combinatorial structures which capture and generalize multiple notions, such as independence in linear algebra, the set of forests of a graph, and algebraic independence in field theory. Moreover, the Bergman fans of matroids correspond to linear spaces in tropical geometry, and by gluing such fans together, one obtains tropical manifolds, i.e. the equivalents of smooth curves and surfaces in regular geometry.
In my thesis, I have investigated how the desirable properties of Bergman fans and tropical manifolds may be generalized. Concentrating on tropical cohomology theory, the tropical Poincaré duality property satisfied by Bergman fans led to a new notion of tropical homology manifolds. These are later shown to be critical in understanding how singular and tropical cohomology are related, and we show how they may be used to study arrangements of curves in the plane.
I hope that tropical homology manifold will continue to prove useful in investigating relations between combinatorics and geometry.
Adjudication committee
- Professor Ilia Itenberg, Sorbonne University
- Professor Helge Ruddat, University of Stavanger
- Associate Professor Jørgen Vold Rennemo, University of Oslo
Supervisors
- Professor Kris Shaw, University of Oslo
- Professor Kristian Ranestad, University of Oslo
Chair of defence
Head of Department Geir Dahl.
Host of the session
Associate Professor Jørgen Vold Rennemo, University of Oslo