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.-
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Trial lecture
4th of February, 12:00, Zoom
"Welschinger invariants in real and tropical enumerative geometry."
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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
Real algebraic geometry is the study of geometric objects defined by polynomial equations with real coefficients. This domain has connections with many areas of mathematics, such as analytic geometry, algebraic topology and analysis, as well as many applications in interdisciplinary fields such as computer-aided design, optimisation, computer vision and robotics. One particularly interesting class of geometric objects for these fields are the hyperbolic varieties, which admits a set of real points/lines/etc where all real lines/planes/etc through this set intersect the variety in a maximal number of real points.
In this thesis, the so-called hyperbolic del Pezzo surfaces are classified by checking the hyperbolicity of some particular curves lying on those surfaces. Several properties of families of real curves are studied from the “logarithmic limit”, which is a particular unbounded graph with straight edges equipped with a “real structure”. We call those limits “real tropical curves”. Using this method, a combinatorial characterisation of the hyperbolicity loci of families of real curves is obtained, as well as several combinatorial criteria for a real curve to have some prescribed number of real components. Finally, some new counter-examples to a conjecture on the arrangement of those real components inside the plane are constructed.
Adjudication committee
Associate Professor Josephine Yu, Georgia Institute of Technology
Associate Professor Cordian Riener, UiT The Arctic University of Norway
Professor Kristian Ranestad, University of Oslo
Supervisors
Associate Professor Kris Shaw, University of Oslo
Professor Frederic Bihan, Université Savoie Mont Blanc
Chair of defence
Head of Department Geir Dahl, University of Oslo
Host of the session
Professor Kristian Ranestad, University of Oslo