This website is devoted to the Spectral Theory Seminar that we are running at the Department of Mathematics, University of Ljubljana.
We meet on Fridays at 14.15 in Classroom 3.06. The talks are streamed to Zoom.
Organizers: Roman Bessonov, Urban Jezernik, Aleksey Kostenko
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A conference in honour of Alexander Volberg's 70th birthday
20 February 2026, 14:15, Classroom 2.03 | Joint with Mathematics Colloquium
Stefan problem is one of the oldest free-boundary problems modelling phase transitions between liquids and solids. If, for example, the solid phase melts in finite time - this is an instance of singularity formation in the language of partial differential equations (PDE). If the rate of melting is self-similar we speak of Type I singularity formation.
After a brief introduction to the Stefan problem, I will show that for an open set of radial initial data the melting rate is to the leading order NOT given by the self-similar scaling. It is instead of Type II with rates predicted in the pioneering work of Herrero and Velazquez. Time remaining, I will explain what we expect to happen in non-radial setting. Our techniques rely on ideas from spectral theory, dynamical systems and PDE.
20.02: Mahir Hadžić (London) [colloquium]
27.02: Marjeta Kramar Fijavž (Ljubljana)
06.03: TBA
13.03: Illia Karabash (Bonn)
20.03: Petr Siegl (Graz)
25.03.: Alexander Volberg (Michigan) [colloquium]
26.03-28.03: Harmonic Analysis Days in Ljubljana
03.04: Seminar vacation
10.04: Jacob Christiansen (Lund)
17.04: Patrick Gerard (Paris) [colloquium]
24.04: TBA
01.05: Praznik dela/Labour day/Vacation
08.05: Markus Reineke (Bochum)
15.05: TBA
22.05: Bor Plestenjak (Ljubljana)
29.05: Gabor Kun (Budapest)
During spring semester, we are happy to have the talks by Jacob Christiansen (Lund), Patrick Gerard (Paris), Mahir Hadžić (London), Enej Ilievski (Ljubljana), Illia Karabash (Bonn), Marjeta Kramar Fijavž (Ljubljana), Gabor Kun (Budapest), Bor Plestenjak (Ljubljana), Markus Reineke (Bochum), Petr Siegl (Graz).
23 January 2026, 14:15, Classroom 3.06
It will be shown that the iterates of an inner function fixing the origin behave as independent random
16 January 2026, 14:15, Classroom 3.06
In the given metric space we choose randomly points (independently of each other and with the same distribution law provided by the given probability measure). Once a finite number of points is chosen, we compute the matrix of squared distances between these points. We are interested in what kind of information on the metric space and the measure can be retrieved from the spectral information (e.g. the spectra and eigenvectors/eigenspaces amd/or their functions, e.g. just the signatures) about the latter matrices. Although there is a lot of open questions in this direction, something can be said. For instance just the signatures of the squared distance matrices determine in which pseudo-euclidean space can one naturally embed isometrically the original metric space. We discuss these questions as well as their relationships with the problems of reconstruction of geometrical structures in the (big) data.