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.-
Submit the request to get access to the thesis (available from 4th March until 18th March 13:15)
Trial lecture
18th of March, time: 11.00 am, room 720 and 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
A tensor is a multi-dimensional data array, occurring ubiquitously in mathematics, physics, engineering and, more generally, in all the situations where one needs to organize data by more than two indices. If tensors remain unchanged after index reordering, they are called symmetric tensors, and in real-life situations they can be simply thought of as homogeneous polynomials of a fixed degree and a given number of variables. A key feature of symmetric tensors is their rank, namely the minimal number of data that is required to fully describe them.
The work of my thesis is concerned with low-dimensional symmetric tensors.
A central role is played by the so-called catalecticant matrices, that store polynomial's coefficients in a suitable order. The first part of my work focuses on the study of some geometric objects, known as reciprocal varieties, which are defined by taking inverses of catalecticant matrices. Points on these varieties are also tensors, and therefore the rank structure is analyzed, together with other relevant geometric properties. The second main topic pertains to alternative notions of rank, which approximate the classical one. Under suitable conditions, I give formulas to compute these invariants via catalecticant matrices of inhomogeneous polynomials.
Adjudication committee
Professor Giorgio Maria Ottaviani, Universita di Firenze
Professor Trygve Johnsen, UiT The Arctic University of Norway
Associate Professor Kris Shaw, University of Oslo
Supervisors
Professor Kristian Ranestad, University of Oslo
Professor John Christian Ottem, University of Oslo
Chair of defence
Professor Erlend Fornæss Wold, University of Oslo
Host of the session
Associate Professor Kris Shaw, University of Oslo