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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7 November 2025 - Seminar is cancelled
07.11: Seminar is cancelled
14.11: Alexander Glazman (Innsbruck)
21.11: TBA
28.11: Marko Žnidarič (Ljubljana)
05.12: Sergei Denisov (Wisconsin)
12.12: Alexander Pushnitski (London)
19.12: TBA
09.01: TBA
16.01: Eugene Stepanov (Pisa & St.Petersburg)
23.01: Artur Nicolau (Barcelona)
24 October 2025, 14:15, Classroom 3.06
Studying spectra of self-similar groups and related questions lead to many important discoveries. Self-similar groups contain examples of groups solving various important open questions, including the Grigorchuk group (the first example of finitely generated groups of intermediate growth), the Basilica group (first example of amenable but not subexponentially amenable groups), and the Lamplighter group (a counterexample to a strong Atiyah conjecture). In this talk I will give an introduction to self-similar groups, discuss methods of studying their spectral properties and spectral properties of associated graphs, and present some results on this topic joint with Rostislav Gigorchuk.
17 October 2025, 14:15, Classroom 3.06
In this talk, I will survey recent advances in the study of universality limits of orthogonal polynomials. I will discuss cases where the Christoffel–Darboux kernel admits a power-law scaling limit. Such universality limits typically arise in the bulk or at the edge of the spectrum. However, we show that at accumulation points of spectral gaps, the scaling behavior can be quite different. In particular, we discuss scaling limits where there is not a unique limiting kernel, but rather a full limit cycle. Balanced measures on real Julia sets of arbitrary expanding polynomials provide natural examples of this type of scaling behavior.
This talk is based on joint works with Milivoje Lukić, Brian Simanek, Harald Woracek and Peter Yuditskii.
10 October 2025, 14:15, Classroom 3.06
This talk is an introduction to the concept of univerasilty in the theory of orthogonal polynomials. We will discuss basic objects and illustrate the usage of universality with one particular example: the nonlinear Carleson problem for Golinski-Ibragimov weights. Recent advances and the current state of art in universality will be presented in the forthcoming talk by Benjamin Eichinger.
3 October 2025, 14:15, Classroom 3.06
I will discuss reversible cellular automata in 1+1 dimensions which describe deterministic interacting particle systems, and present several nontrivial examples that show certain aspects of integrability. Most notable is the reversible Rule 54, for which one can obtain exact matrix product expressions for probability state vectors in various setups, ranging from nonequilibrium steady state of the system coupled to markovian stochastic boundaries (and completely diagonalizing the corresponding markov chain) to time-dependent statistical ensembles.
I will present also two deformations which turn the model into either quantum or stochastic cellular automaton. Both deformations, being parametrixed by an arbitrary unitary or stochastic 2x2 matrix, respectively, exhibit some features of integrability. The later (stochastic version) can be interpeted as a lattice discretization of deformed polynuclear growth model. Depending on the remaining time, I will discuss the construction of non-trivial conservation laws of the quantum deformation and/or the matrix product form of the steady state of the boundary driven stochastic deformation.