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 24th of July 1:15 pm until 7th of August 1:15 pm)
Trial lecture
7th of August, time: 10:15 am, room 1259 (Abels utsikt) and zoom.
- 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.
In enumerative geometry, we compute various types of invariants in order to distinguish different geometries. The best-known such invariant counts the numbers of holes in a space. To distinguish geometries, which differ in more subtle ways, one source of invariants is viewing the given geometry as the underlying space of a physical theory and computing physical invariants.
A modern incarnation of this are algebraic curve-counting theories inspired by string theory. String theory views particles as 1-dimensional strings in space. Evolving over time, they span a 2-dimensional surface inside 10-dimensional space-time, which consists of usual 4-dimensional space-time together with six additional dimensions. Imposing certain physical conditions, this surface must be a complex algebraic curve inside a compact complex Calabi-Yau 3-fold, which comprises the extra dimensions. Studying particles in string theory is thus intimately connected to curve-counting in algebraic geometry.
One curve-counting theory is Donaldson-Thomas theory, where we count 1-dimensional subvarieties. In this thesis, we study generating series of K-theoretically refined Donaldson-Thomas invariants, which involve more intricate geometric information than more classical numerical Donaldson-Thomas invariants. We compute the refined generating series of a certain orbifold geometry explicitly using factorization. We also prove a correspondence between two types of refined invariants using wall-crossing.
Adjudication committee
- Assistant Professor Andrea Ricolfi, SISSA
- Chargé de recherche Tudor Pădurariu, Sorbonne University
- Professor Kristian Ranestad, University of Oslo
Supervisors
- Associate Professor Jørgen Vold Rennemo, University of Oslo
- Professor John Christian Ottem, University of Oslo
Chair of defence
Head of Department Geir Dahl.
Host of the session
Professor Kristian Ranestad, University of Oslo