17.04.2024, 13:00
– Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie
Zero measure Cantor spectrum for Sturmian metric graphs
Gilad Sofer (Technion)
Gilad Sofer (Technion)
Jonathan Taylor (UP)
Abstract: Given a directed row-finite graph, one may define representations of such a graph in C*-algebras and deduce the existence of a unique C*-algebra that is universal for such representations....
mehr erfahrenAnna Muranova (University of Warmia and Mazury in Olsztyn)
Abstract: In this talk we consider graphs, whose weights belong to an ordered field. It is known, that in the case of real weights every weighted graph defines a Markov chain, whose states are...
mehr erfahrenKonstantin Pankrashkin (Carl von Ossietzky Universität Oldenburg)
Abstract: For a class of weighted infinite metric trees we propose a definition of the boundary trace which maps H^1-functions on the tree to L^2-functions on a compact Riemannian manifold. For a...
mehr erfahrenProf. Olaf Post (Trier)
Abstract: In this talk I will present a construction of discrete magnetic non-isomorphic graphs with isospectral Laplacians. The construction is based on gluing building blocks according to a...
mehr erfahrenSimon Barthelmé
Abstract: Joint work with Nicolas Tremblay, Pierre-Olivier Amblard
Determinantal Point Processes (DPPs) are an important class of models of random sets that arise in many areas of mathematics and...
Renaud Leplaideur (Université de la Nouvelle-Calédonie)
Abstract: I will present a new object, called substreetution, which is an extension of substitutions in dynamics (Z-action) to colored trees (free-group action). The main part of the talk will be...
mehr erfahrenPaul Hege (Tübingen)
Abstract: The spectrum of infinite-volume operators is often computed numerically by considering finite sections with Dirichlet or periodic boundary conditions, but such artificial boundary conditions...
mehr erfahrenDr. Christian Seifert (TUHH)
Abstract: Given a radial metric tree graph, we consider Laplacians with self-adjoint coupling conditions at the vertices. We consider the questions whether presence of absolutely continuous spectrum...
mehr erfahrenOfir David (Technion)
Abstract: In 1978, Apery proved the irrationality of the Riemann zeta value ζ(3) by utilizing a fast converging sequence of rational approximations. However, the details of his proof remained...
mehr erfahrenUjjal Das (Technion)
The abstract can be found here.
mehr erfahrenSelim Sukhtaiev (Auburn University)
Abstract: This talk is centered around a symplectic approach to eigenvalue problems for systems of ordinary differential operators (e.g., Sturm-Liouville operators, canonical systems, and quantum...
mehr erfahrenJohannes Happich (Leipzig)
Abstract: When comparing the complexity of different aperiodic quasicrystals, it appears that linear repetitivity is a useful property that only applies to the - in some sense - most regular...
mehr erfahrenGregory Berkolaiko
Abstract:
Eigenvalue interlacing is a tremendously useful tool in linear algebra
and spectral analysis. In its simplest form, the interlacing
inequality states that a rank-one positive perturbation...
James Kennedy
Abstract: SMPs offer a way of dividing a given object (domain, manifold or graph) into a given number of pieces in an ``analytically optimal'' way: typically, one attempts to minimise an energy...
mehr erfahrenDr. Christian Rose (Potsdam)
Abstract: On Riemannian manifolds the conjunction of Gaussian upper heat kernel bounds and the volume doubling property of balls are equivalent to Sobolev inequalities in arbitrarily small balls. The...
mehr erfahrenMarvin Weidner (Barcelona)
Abstract: The celebrated De Giorgi-Nash-Moser theory establishes Hölder regularity of solutions to second order equations in divergence form without any regularity assumptions on the coefficients....
mehr erfahrenGilad Sofer (Technion)
Abstract: Sturmian Hamiltonians appear in mathematical physics as popular models for one-dimensional quasicrystals. This family of discrete quasiperiodic Schrödinger operators, including the well...
mehr erfahrenFlorian Fischer (Potsdam)
Abstract: We show various sharp Hardy-type inequalities for the linear and quasi-linear Laplacian on non-compact harmonic manifolds with a particular focus on the case of Damek-Ricci spaces. Our...
mehr erfahrenMatti Richter (Potsdam)
Abstract: We study positive generalized eigenfunctions of Schrödinger operators associated to graphs with cocompact group actions of nilpotent groups. For such a graph, we investigate the topological...
mehr erfahrenProf. Dr. Peter Stollmann (Chemnitz)
Abstract: We report on recent results from a joint work with B. Güneysu, S. Pigola and. G. Veronelli. Using a new notion of subharmonicity we can prove a version of the Braverman-Milatovic-Shubin...
mehr erfahrenDr. Ulrik Enstad (Stockholm University)
Abstract: Many structured function systems in harmonic analysis arise from the action of a unitary group representation on a single vector in the underlying Hilbert space. A central question is...
mehr erfahrenShubham Gupta
Abstract: In the continuum, symmetrization inequalities are a fundamental tool in various parts of analysis: variational problems, spectral geometry, mathematical physics just to name a few. In this...
mehr erfahrenProf. Yehuda Pinchover (Technion)
Abstract: Let p ∈ (1,∞) and Ω⊂ℝN be a domain.
Let A:=(aij) ∈ L∞loc(Ω ; ℝN× N) be a symmetric and locally uniformly positive definite matrix. Set |ξ|A2:= ∑i,j=1N aij(x) ξi ξj, ξ ∈ ℝN, and let V be...
mehr erfahrenProf. Ron Rosenthal (Technion)
Abstract: In the talk we will introduce a model for random simplicial complexes which are high-dimensional counterparts of random regular graphs.
We will present some results for such random complexes...
mehr erfahrenBernard Helffer (Nantes Université)
in collaboration with
G. Berkolaiko, G. Cox, and M. Persson Sundqvist
Abstract
Recent work of the authors and their collaborators has uncovered fundamental connections between the...
Anna Muranova (University of Warmia)
Abstract:
We consider discrete normalized Laplacian for finite graphs, whose edge-weights belong to an arbitrary real-closed ordered field. We show that eigenvalues of Laplacian always belong to the...
Borbola Gerhat (Prague)
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Tanja Eisner (Leipzig)
Abstract: We discuss a proof of multiple recurrence for ergodic systems (and thereby of Szemerédi's theorem) being a mixture of three known proofs. It is based on a conditional version of the...
mehr erfahrenChristian Seifert (Technische Universität Hamburg)
Abstract: Given an abstract Cauchy problem in a Banach space we consider two questions:
1. Can we steer the system to any given state (or to zero, say) in finite time by some inhomogeneity?
2. Can we...
Xueping Huang (Nanjing University)
Abstract: We consider the discrete analogue of semi-linear differential inequalities on weighted graphs. Under some technical conditions, we obtain almost sharp volume growth criteria for the...
mehr erfahrenChristoph Richard (Erlangen)
Abstract: We define a notion of uniform density on translation bounded measures in unimodular amenable locally compact Hausdorff groups, which is based on a group invariant introduced by Leptin in...
mehr erfahrenAnton Gorodetski (UCI)
Abstract: In this talk we will formulate a non-stationary version of the Furstenberg Theorem on random matrix products. As a main application we will discuss how it can be used to prove a...
mehr erfahrenNoema Nicolussi (Potsdam)
There are many interesting parallels between analysis on Riemann surfaces and graphs. Both settings admit a Laplace operator and the Poisson equation reflects crucial geometric information.
Motivated...
mehr erfahrenProf. Daniel Lenz (Universität Jena)
Abstract: Uniformity of continuous SL(2,R) valued cocycles over uniquely dynamical systems has featured in various contexts. Walters asked in '86 whether every uniquely ergodic system admits a...
mehr erfahrenAli Ben Amor (Gabès, Tunisia)
Shiwen Zhang (University of Minnesota)
Abstract: The localization landscape theory, introduced in 2012 by Filoche and Mayboroda, considers the landscape function u solving Hu=1 for an operator H. The landscape theory has remarkable power...
mehr erfahrenTatiana Smirnova-Nagnibeda (Genf)
Abstract: In this talk we will discuss some results in the spectral theory of infinite graphs obtained using techniques coming from the study of self-similar groups and their actions.
mehr erfahrenBobo Hua (Fudan University Shanghai)
Abstract: We prove sharp l^2 decay estimates of nonnegative generalized subharmonic functions on graphs with positive Laplacian spectrum, which generalizes the result by Li and Wang on Riemannian...
mehr erfahrenFlorentin Münch
Florentin Münch (MPI Leipzig)
Christian Rose (Universität Bremen)
Abstract: The heat kernel as the minimal fundamental solution of the heat equation is one of the most important objects studied in geometric analysis and encodes the geometry of the underlying space...
mehr erfahrenDaniel Lenz (Jena)
Philipp Hake (Leipzig)
Elias Zimmermann (Leipzig)
Safoura Zadeh (MFO Leibniz Fellow)
Please contact Siegfried Beckus (beckus@uni-potsdam.de) if you are interested to join the talk.
mehr erfahrenTanja Eisner (Leipzig)
Title: Wiener's lemma along subsequences.
Abstract: We discuss the validity of the classical Wiener lemma and the extremal behaviour of a measure on the unit circle via the behavior of its Fourier...
Alexey Klimenko
Please contact Siegfried Beckus (beckus@uni-potsdam.de) if you are interested to join the talk.
mehr erfahrenJean Bellissard (University of Münster)
Please contact Siegfried Beckus (beckus@uni-potsdam.de) if you are interested to join the talk.
mehr erfahrenAlexander Grigor'yan (University of Bielefeld)
Please contact Siegfried Beckus (beckus@uni-potsdam.de) if you are interested to join the talk.
mehr erfahrenMatti Richter
Dr. Siegfried Beckus (Universität Potsdam)
Uzy Smilansky (Weizmann Institute of Science)
Trace formulae are one of the most important tools in a large number of fields ranging from quantum chaos via spectral geometry, graphs and number theory. Here, I shall present two rather...
mehr erfahrenDr. Christian Rose (MPI Leipzig)
The Kato condition on the negative part of the Ricci curvature turned out to be an appropriate generalization of Lp- curvature conditions that can be used to investigate geometric and topological...
mehr erfahrenAnna Muranova (Bielefeld University)
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Bernard Helffer (University of Paris-Sud)
Abstract: We revisit Courant's nodal domain property for linear combinations of eigenfunctions. This property was proven by Sturm (1836) in the case of dimension 1. Although stated as true for the...
mehr erfahrenMax Kämper (TU Dortmund)
Random Schrödinger operators are a model for metals with random impurities and this talk will present them for the special case of the Anderson operator on a lattice. We will introduce the integrated...
mehr erfahrenNoema Nicolussi (University of Vienna)
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Prof. Dr. Ram Band (Israel Institute of Technology - Technion)
We discuss the number of zeros of Laplacian eigenfunctions on a metric (quantum) graph.
The n-th eigenfunction has at least n-1 zeros and at most n-1+\beta zeros, where \beta is the number of graph...
Philipp Bartmann
We will discuss aspects of classical interpolation theory including properties of the Hardy–Littlewood maximal function and Marcinkiewicz’s interpolation theorem. Further, we will establish the...
mehr erfahrenJonas Grünberg
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Christian Scholz
Consider a countable set and a weighted, uniformly locally finite graph. In his paper "Parabolic Harnack inequality and estimates of Markov chains on graphs", Delmotte proves that parabolic Harnack...
mehr erfahrenMichael Schwarz
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Magda Khalile (Leibniz Universität Hannover)
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Marc Hellmuth (Universität Greifswald)
Phylogenomics aims at finding plausible hypothesis about the evolutionary history of gene or species based on genomic sequence information. Genes are passed from generation to generation to the...
mehr erfahrenFlorian Fischer (Universität Potsdam)
In the classical potential theory on Euclidean space and in the potential theory of transient Markov chains a unique decomposition of superharmonic functions in a harmonic and a potential part is...
mehr erfahrenChristian Rose (Technische Universität Chemnitz)
We show that if the negative part of the Ricci curvature of a compact manifold is in the Kato-class, the Cheeger constant of the manifold can be bounded below by a positive constant. This is obtained...
mehr erfahrenSiegfried Beckus (Universität Potsdam)
The celebrated Shnol theorem asserts that every polynomially bounded generalized eigenfunction for a given energy E associated with a Schrödinger operator H implies that E is in the L2-spectrum of H....
mehr erfahrenMelchior Wirth
Michael Hinz (Bielefeld)
In this talk we review the definitions of items of vector calculus based on Dirichlet forms and mention connections to graph Laplacians and to non-local and local operators on metric measure spaces....
mehr erfahrenDorothee Schüth (HU Berlin)
Jan Maas (IST Austria)
Michael Schwarz
Florentin Münch
We give rigidity results for discrete Bonnet-Myers diameter bound and Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a hypercube. The proofs use...
mehr erfahrenMoritz Gerlach
This talk aims at completing the picture how exactness of dynamical systems is related to the asymptotic behavior of the Perron-Frobenius operator. In doing so, we give a mixing-like description of...
mehr erfahrenFelix Pogorzelski (Technion Haifa)
Radoslaw Wojciechowski (CUNY)
Shiping Liu (Durham)
I will discuss a Buser type and a Lichnerowicz type eigenvalue estimates for the magnetic Laplacian on a closed Riemannian manifold. Those are motivated by our previous ...
mehr erfahrenChristian Seifert (Hamburg Harburg)
We consider families of bounded linear operators on \ell_p-spaces of discrete groups, parametrized by a dynamical system. By using limit operator techniques, we show that all the operators from that...
mehr erfahrenMarkus Kunze (Konstanz)
We consider diffusion problems in a domain which is further subdivided by semi-permeable membranes. Such problems frequently occur in applications in biology, for example when studying the...
mehr erfahrenMartin Schuhmacher
Felix Knöppel (TU Berlin)
Batu Güneysu (HU Berlin)
Elke Rosenberger (Potsdam)
Siegfried Beckus (University Jena)
Christian Rose (TU Chemnitz)
Michela Egidi (TU Chemnitz)
In this talk (joint work with O. Post) we consider a family of compact, oriented and connected n-dimensional manifolds constructed according to the ...
mehr erfahrenFrancesco Tudisco (Saarland University)
This introductory talk will focus on the eigenvalues and eigenfunctions of the graph p-Laplacian. We shall discuss two definitions of the eigenpairs that come as a natural generalization of the linear...
mehr erfahrenJochen Glück (Universität Ulm)
Let T = (T(t)) be a C_0-semigroup on some function space or, more generally, on a Banach lattice E. The semigroup T is called positive if T(t)f \ge 0 for each 0 \le f \in E and for each t \geg 0....
mehr erfahrenJun Masamune (Tohoku University)
When every harmonic function belonging to a space $E$ of functions is identically constant, we say that the $E$-Liouville property holds true. There are different types of Liouville property according...
mehr erfahrenFelix Pogorzelski (Technion Haifa)
Marcel Schmidt (University Jena)
Michael Schwarz (Potsdam)
We consider weighted graphs with an infinite set $X$ of vertices such that every function of finite energy is bounded. For each of these graphs there is a compact set $K$ containing $X$ as a dense...
mehr erfahrenFlorentin Münch (Potsdam)
We introduce a new version of curvature dimension inequality. We use this to prove a logarithmic Li-Yau inequality on graphs. To formulate this inequality, we use a non-linear ariant of the calculus...
mehr erfahrenMoritz Gerlach (Potsdam)
Given a finite sequence of n samples drawn independently at random from a compact submanifold of the Euclidean space, we study the asymptotic behavior of Laplacians on the epsilon-neighborhood graph...
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