TU Dortmund
Fakultät für Mathematik

Prof. Dr. Ivan Veselić - Talks

2020

TitleUncertainty relations, control theory and perturbation of spectral bands
InstitutionDepartment of Mathematical Sciences, University of Durham, England
OccasionAnalysis and/of PDE Seminar
Date5. November 2020, 15:00 CET
AbstractSlides of the talk are provided here.

 

TitleQuantitative unique continuation estimates and resulting uncertainty relations for Schroedinger and divergence type operators
InstitutionDepartment of Mathematical Sciences, University of Bath
OccasionResearch seminar: Asymptotics, operators, and functionals
Date12. October 2020, 17:15-19:45 CEST
AbstractThe talk is devoted to quantitative unique continuation estimates and resulting uncertainty relations of solutions of elliptic differential equations and eigenfunctions of associated differential operators, as well as linear combinations thereof. Such results have recently been successfully applied in several fields of mathematical physics and applied analysis: control theory, spectral engineering of eigenvalues in band gaps, and Anderson localization for random Schroedinger operators. In this talk we will focus on properties of functions in spectral subspaces of Schroedinger operators. At the end we will give some results which apply to more general elliptic second order differential equations.

 

TitleScale-free uncertainty relations and applications in spectral and control theory
InstitutionBrijuni, Croatia
OccasionTenth Conference on Applied Mathematics and Scientific Computing
Date15. September 2020
AbstractWe present an uncertainty relation for spectral projectors of Schroedinger operators on bounded and unbounded domains. These have sevaral applications, among others in the spectral theory of random Schroedinger operators. Here we will present two applications which are likely to be of interest to the audience of the conference: Shifting of bands of the essential spectrum and of eigenvalues of Schroedinger operators and controllability of the heat equation.

 

TitleScale-free uncertainty relations for spectral projectors and applications
InstitutionInstitut für Mathematik der Humboldt-Universität zu Berlin
OccasionWorkshop: Analytical Modeling and Approximation Methods
Date5. March 2020

 

2019

TitleUpper and lower Lipschitz bounds for shifting the edges of the essential spectrum of Schroedinger operators
InstitutionUniversité Côte d'Azur / Laboratoire Mathématiques & Interactions J.A. Dieudonné
OccasionSéminaire de l'équipe EDP Analyse Numérique
Date28. November 2019
AbstractThe spectrum of periodic Schroedinger operators is well known to consist of bands of essential spectrum separated by gaps, which belong to the resolvent set. The periodicity assumption allows to exhibit much more delicate properties of the spectrum, e.g. it is purely absolutely continuous. In this talk we consider the situation that the Schroedinger operator exhibits several bands of essential spectrum, but that no periodicity is assumed. This allows then for eigenvalues in the intervals between essential spectrum components. We study how the edges of the essential spectrum (and the eigenvalues in essential gaps) are shifted when a semi-definite potential is added. Crucial ingredients in the proof are a scale-free uncertainty relation and variational principles for eigenvalues in gaps of the essential spectrum.

 

TitleUpper and lower Lipschitz bounds for perturbation of the edges of the essential spectrum
InstitutionSveučilište u Dubrovniku
OccasionSeminar za primijenjenu matematiku i teoriju upravljanja
Date29. August 2019
AbstractPeriodic Schroedinger operators have spectrum consisting of closed intervals as connected components. These are called spectral bands. They correspond to energies where transport is possible in the medium modelled by the Schroedinger operator. For this reason it is of interest to study perturbation of spectral bands. On the one hand, one wants to establish that for small perturbations the band will not move too much. On the other hand, for perturbations with fixed sign it possible to ensure that band edges will indeed move by a quantifiable amount. This makes spectral engineering possible. We report on such results based on unique continuation principles and variational principles for eigenvalues in gaps of the essential spectrum.

 

TitleSpectral inequalities and null control for the heat conduction problem on domains with multiscale structure
InstitutionUniversität Bonn
Date5. July 2019
AbstractI discuss uncertainty relations (aka spectral inequalities) for the Laplace and Schroedinger operators on bounded and unbounded domains. The subset of observation is assumed to be a thick or an equi-distrubuted set. A new result on the control cost allows to apply the first mentioned results and study the behaviour of the control cost in several asymptotic regimes, both regarding time and geometry.

 

TitleUncertainty relations and null control for the heat conduction problem on domains with multiscale structure
InstitutionFern-Universität Hagen
OccasionConference "On mathematical aspects of interacting systems in low dimension"
Date24. June - 27. June 2019
AbstractI discuss uncertainty relations (aka spectral inequalities) for the Laplace and Schroedinger operators on bounded and unbounded domains. The subset of observation is assumed to be a thick or an equi-distrubuted set. A new result on the control cost allows to apply the first mentioned results and study the behaviour of the control cost in several asymptotic regimes, both regarding time and geometry. Methodical analogies to the study of random Schroedinger operators are highlighted.

 

TitleUpper and lower Lipschitz bounds for perturbation of the edges of the essential spectrum
InstitutionFern-Universität Hagen
OccasionOberseminar Mathematische Physik
Date2. April 2019

 

TitleNull-controllability of the heat equation on bounded and unbounded domains
InstitutionTU Dortmund
OccasionOberseminar Numerische Analysis und Optimierung
Date14. March 2019

 

2018

TitleWegner estimate for Landau-breather Hamiltonians
InstitutionPontificia Universidad Catolica de Chile
OccasionSpectral Theory and PDE Seminar
Date13. December 2018
AbstractI discuss Landau Hamiltonians with a weak coupling random electric potential of breather type. Under appropriate assumptions a Wegner estimate holds. It implies the Hölder continuity of the integrated density of states. The main challenge is the problem how to deal with non-linear dependence on the random parameters.

 

TitleScale free unique continuation estimates with three applications
InstitutionPontificia Universidad Catolica de Chile
OccasionInternational Conference "Spectral Theory and Mathematical Physics 2018"
Date06. December 2018
AbstractI will present scale free unique continuation estimates for functions in the range of any compact spectral interval of a Schroedinger operator on generalized parallelepipeds. The latter could be cubes, halfspaces, octants, strips, slabs or the whole space. The sampling set is equidistributed. The unique continuation estimates are very precise with respect to the energy, the potential, the coarsenes scale, the radius defining the equidistributed set and actually optimal in some of these parameters. Such quantitative unique continuation estimates are sometimes called uncertainty relations or spectral inequalities, in particular in the control theory community. These estimates have range of applications. I will present three. The first concerns lifting of edges of components of the essential spectrum, the second Wegner estimates for a variety of random potentials, and the last one control theory of the heat equation. The talk is based on joint works with Nakic, Taeufer and Tautenhahn, and loosely related with works with Egidi and Seelmann.

 

TitleUncertainty principles and null-controllability of the heat equation on bounded and unbounded domains
InstitutionUniversity of Split
OccasionApplMath18 Ninth Conference on Applied Mathematics and Scientific Computing, Solaris, Sibenik, Croatia
Date17. September - 20. September 2018
AbstractIn the talk I discuss several uncertainty relations for functions in spectral subspaces of Schrödinger operators, which can be formulated as (stationary) quantitative observability estimates. Of particular interest are unbounded domains or (a sequence of) bounded domains, with multi-scale structure and large diameter. The stationary observability estimates can be turned into control cost estimates for the heat equation, implying in particular null-controlability. The interesting question in the context of unbounded domains is: Which geometric properties needs a observability set to have in order to ensure null-controlability and efficient control cost estimates? The talk is based on two joint projects, one with I. Nakić, M. Täufer, and M. Tautenhahn, the other with M. Egidi.

 

TitleNull controllability for the heat equation
InstitutionUniversity of Split
OccasionSplitsko matematicko drustvo
Date14. September 2018
AbstractIn the talk I discuss several uncertainty relations for functions in spectral sub- spaces of Schrödinger operators, which can be formulated as (stationary) quanti- tative observability estimates. Of particular interest are unbounded domains or (a sequence of) bounded domains, with multi-scale structure and large diameter. The stationary observability estimates can be turned into control cost estimates for the heat equation, implying in particular null-controllability. In particular, I will discuss sufficient and — in the case of the pure heat equation actually — sharp geometric criteria for null-controllability. The talk is based on joint projects with M. Egidi, A. Seelmann, I. Nakić, M. Täufer, and M. Tautenhahn.

 

TitleUpper and lower Lipschitz bounds for the perturbation of edges of the essential spectrum
InstitutionUniversitaet Bielefeld
OccasionKolloquium Mathematische Physik
Date01. June 2018
AbstractLet A be a selfadjoint operator,B a bounded symmetric operator and A+tB a perturbation. I will present upper and lower Lipschitz bounds on the function of t which locally describes the movement of edges of the essential spectrum. Analogous bounds apply also for eigenvalues within gaps of the essential spectrum. The bounds hold for an optimal range of values of the coupling constant t. This result is applied to Schroedinger operators on unbounded domains which are perturbed by a non-negative potential which is mostly equal to zero. Unique continuation estimates nevertheless ensure quantitative bounds on the lifting of spectral edges due to this semidefinite potential. This allows to perform spectral engineering in certain situations. The talk is based on this preprint.

 

TitleUniform Approximation of the integrated density of states on amenable groups
InstitutionBergische Universitaet Wuppertal
OccasionWorkshop Ergodic Theory
Date05. May 2018

 

TitleNecessary and sufficient geometric condition for null-controllability of the heat equation on $\Bbb R^d$.
InstitutionFernuni Hagen
OccasionWorkshop on "Control theory of infinite-dimensional systems"
Date10. January - 12. January 2018
AbstractIn this talk we discuss the control problem for the heat equation on $\Bbb R^d, d \geq 1$, with control set $\omega \subset \Bbb R^d$. We provide a sufficient and necessary condition (called $(\Gamma, a)$-thickness) on $\omega$ such that the heat equation is null-controllable. We give an estimate of the control cost with explicit dependency on the characteristic geometric parameters of the control set. Finally, we derive a control cost estimate for the heat equation on cubes with periodic, Dirichlet, or Neumann boundary conditions, where the control sets are again assumed to be thick. We show that the control cost estimate consistent with the $\Bbb R^d$ case. (This is joint work with Michela Egidi.)

 

2017

TitleGlivenko Cantelli and Ergodic Theorem on groups.
InstitutionRuhr Uni Bochum (RUB)
OccasionRTG 2131-Seminar
Date23. October 2017

 

TitleGlivenko Cantelli and Banach-space ergodic theorems applied to the uniform approximation of the integrated density of states
InstitutionUniversität Trier
OccasionFrench-German meeting Aspect 17: Asymptotic Analysis and Spectral Theory
Date25. September - 29. September 2017
AbstractThe integrated density of states is the cumulative distribution function of the spectral measure of a random ergodic Hamiltonian. It can be approximated by cumulative distribution functions associated to finite volume Hamiltonians. We study uniform convergence for this approximation in the case where the Hamiltonian is defined on an Euclidean lattice, or more generally, on a discrete amenable group. We obtain a convergence estimate which can be seen as a special case of a Banach space valued Ergodic Theorem. Our proof relies on multivariate Glivenko-Cantelli Theorems. (This is joint work with Christoph Schumacher and Fabian Schwarzenberger.)

 

TitleGlivenko-Cantelli Theory, Banach-space valued Ergodic Theorems and uniform approximation of the integrated density of states
InstitutionUniversität Potsdam
OccasionInternational Conference on Analysis and Geometry on Graphs and Manifolds
Date31. July - 04. August 2017
AbstractThe integrated density of states is the cumulative distribution function of the spectral measure of a random ergodic Hamiltonian. It can be approximated by cumulative distribution functions associated to finite volume Hamiltonians. We study uniform convergence for this approximation in the case where the Hamiltonian is defined on an Euclidean lattice, or more generally, on a discrete amenable group. We obtain a convergence estimate which can be seen as a special case of a Banach space valued Ergodic Theorem. Our proof relies on multivariate Glivenko-Cantelli Theorems. (This is joint work with Christoph Schumacher and Fabian Schwarzenberger.)

 

TitleUnique continuation estimates and lifting of eigenvalues.
InstitutionEuler Institute, Saint-Petersburg, Russia
Occasion9th Birman Conference in Spectral Theory
Date03. July - 06. July 2017
AbstractUsing Carleman estimates we prove scale free unique continuation estimates on bounded and unbounded domains and apply them to the spectral theory of Schroedinger operators. Inparticluar, we present eigenvalue lifting estimates and lifting estimates for spectral band edgesof periodic and similar Schroedinger operators. This is joint work with I. Nakic, M. Taeufer, and M. Tautenhahn.

 

TitleDichotomy for the expansion of the deterministic spectrum of random Schroedinger operators
InstitutionBergische Universität Wuppertal
OccasionHagen-Wuppertal Analysis-Treffen
Date2. May 2017

 

TitleUnique continuation estimates and the Logvinenko Sereda Theorem.
InstitutionFernuni Hagen
OccasionOberseminars Stochastik/Mathematische Physik
Date15. February 2017
AbstractUnique continuation estimates for solutions of partial differential equations are a topic of classical interest. More recently they have turned out to have important applications for Schroedinger operators modelling condensed matter. We will present a scale-free unique continuation estimate which is tailored for such applications. Holomorphic functions exhibit unique continuation properties as well, even more precise ones. This motivates the question, to what extent UCP for solutions of PDEs can be raised to the same level as UCP for holomorphic functions. We give some partial results in this direction.

 

2016

TitleUnique continuation estimates and the Logvinenko Sereda Theorems
InstitutionUniversite de Strasbourg
OccasionSeminaire d' Analyse
Date13. December 2016
AbstractUnique continuation estimates for solutions of partial differential equations are a topic of classical interest. More recently, they have turned out to have important applications for Schroedinger operators modelling condensed matter. We will present a scale-free unique continuation estimate that is tailored for such applications. Holomorphic functions exhibit unique continuation properties as well, even more precise ones. This motivates the question to what extent UCP for solutions of PDEs can be raised to the same level as UCP for holomorphic functions. We give some partial results in this direction.

 

TitleUnique continuation principle and its absence on continuum and discrete geometries
InstitutionTechnische Universität Wien
OccasionWorkshop on Operator Theory and Indefinite Inner Product Spaces
Date12. December 2016
AbstractA powerful tool in the analysis of solutions of partial differential equations are unique continuation principles. Quantitative versions play an important role in inverse problems, uniqueness theorems for linear and non-linear differential equations, and in the theory of random Schroedinger operators. On the contrary quantum graphs violate the continuation principle, giving rise to new phenomena. Certain graph Laplacians exhibit similar features.

 

TitleUncertainty relations and applications to the Schrödinger and heat conduction equations
InstitutionJohannes Gutenberg Universität Mainz
OccasionSummer school Mainz
Date13. September 2016
AbstractIn four lectures we discuss unique continuation principles for various classes of functions, their relation to uncertainty principles, and their application in the analysis of certain elliptic and parabolic partial differential equations. We are in particular interested in domains and coefficient functions which have a multiscale structure as it istypical for periodic and random Schrödinger operators. The first two lectures are held by Ivan Veselic, the third by Martin Tautenhahn, and the last by Michela Egidi.

 

TitleA dummies view on compressive sensing
InstitutionUniversity of Split School of Medicine, Split, Croatia
OccasionSummer school Split
Date27. August - 03. September 2016

 

TitleUnique continuation principle and its absence on continuum space, on lattices and on quantum graphs
InstitutionWIAS Berlin
OccasionNewMET 2016
Date14. July - 15. July 2016
AbstractA powerful tool in the analysis of solutions of partial differential equations are unique continuation principles. Quantitative versions play an important role in inverse problems, uniqueness theorems for linear and non-linear differential equations, and in the theory of random Schroedinger operators. On the contrary quantum graphs violate the continuation principle, giving rise to new phenomena. Certain graph Laplacians exhibit similar features.

 

TitleMultiscale equidistribution estimates for Schr ̈odinger eigenfunctions
InstitutionDepartment of Mathematics, Faculty of Science, University of Zagreb, Croatia
OccasionInternational Workshop on PDEs: analysis and modelling Celebrating 80th anniversary of professor Nedžad Limić
Date19. June - 22. June 2016
AbstractWe present two results on scale-free quantitative unique continuation of eigenfunctions of the Schr̈odinger operator and linear combinations thereof. The first result is dueto Rojas-Molina & Veselić, the generalization to linear combinations of eigenfunctions to Nakić, Taeufer, Tautenhahn, & Veselić. We will sketch the proof for the case of pure eigenfunctions. It relies on Carleman estimates, three annuli inequalities and geometric covering arguments

 

TitleQuantitative uncertainty principles in harmonic analysis and mathematical physics
Occasion6th Croatian Mathematical Congress
Date16. June 2016
AbstractIn harmonic analysis the uncertainty principle asserts that it is impossibe that a function as well as its Fourier transform are simultaneously compactly supported. In quantum mechanics the uncertainty principle asserts that it is impossible to measure two conjugate observables with arbitraty precision simultaneously. We present recent quantitative versions of uncertainty principles as well as their relations and applications in the theory of partial differential equations and random Schroedinger operators.

 

Title(Miss)Verständnis der Stochastik
InstitutionFern-Universität Hagen
OccasionSeminar Stochastik
Date4. January 2016

 

2015

TitleWeihnachtsvorlesung "(Miss)Verständnis der Stochastik"
InstitutionTechnische Universität Chemnitz
OccasionWeihnachtsvorlesung am Tag der Lehre
Date3. December 2015, 15:30 bis 17:00, Zentrales Hörsaalgebäude, Raum N112.
AbstractWeihnachtsvorlesung zu Themen der Stochastik für ein breites Publikum

 

TitleHadamard's three line theorem and Carleman estimates (Hadamardov teorem of tri pravca i Carlemanove ocjene)
InstitutionZagreb University , Mathematics department
OccasionColloquium of the Croatian Mathematical Society
Date30. September 2015, 17:00
AbstractWe start with the maximum modulus principle for holomorphic functions and deduce Hadamard's three line theorem and Hadamard's three circle theorem. Then we pursue the question, which of these properties are shared by solutions of elliptic partial differential equations. Without proof we state a Carleman estimate and an interpolation inequality which follows. Applications thereof are discussed, time permitting, at the end of the talk.
Linkhttp://degiorgi.math.hr/kolokvij/view.php?id=121

 

TitleUniform ergodic theorems and the Glivenko-Cantelli theorem (Uniformni ergodički teoremi i Glivenko Cantellijev teorem)
InstitutionZagreb University , Mathematics department
OccasionProbabilty seminar
Date29. September 2015, 14:30
Linkhttps://web.math.pmf.unizg.hr/zzvs/?Seminars

 

TitleApproximation and estimation of functions based on local data (Aproksimacija i ocjena funkcija na osnovu lokalnih podataka)
InstitutionRijeka University, Department of Natural Sciences and Mathematics
OccasionColloquium of the society of mathematicians and physicists
Date28. September 2015, 12:00
AbstractIn many areas of mathematics and its application in other sciences one is confronted with the task of estimating or reconstructing a function based on partial local data. Of course, this will not work for all functions well. Thus one needs an restriction to an adequate class of functions. This can be mathematically modeled in many ways. Spacial statistics or complex function theory are relevant areas of mathematics which come to ones mind. We present several results on reconstruction and estimation of functions which are solutions of elliptic partial differential equations on some subset of Euclidean space. We comment also on analogous statements for functions with localized Fourier transform.
Link http://dmf.hr/2015/06/19/aproksimacija-i-ocjena-funkcija-na-osnovu-lokalnih-podataka/

 

TitleUncertainty relations and applications (Relacije neodređenosti i primjene)
InstitutionUniversity of Split
OccasionSeminar of the Split mathematical society
Date18. September 2015, 12:00
Linkhttp://www.stmath.hr/?p=654

 

TitleCompressed sensing and the Calderon problem in electrical impedance tomography
InstitutionUniversity of Split
OccasionSpeech and Hearing Research Lab, School of Medicine
Date17. September 2015, 11:00
Link http://kovaciclab.org/seminar-prof-dr-sc-ivan-veselic-compressed-sensing-calderon-problem-on-electrical-impedance-tomography/

 

TitleGlivenko-Cantelli theory for almost additive functions and Banach space-valued ergodic theorems on lattices
InstitutionFriedrich-Alexander-Universität Erlangen-Nürnberg
OccasionTag der Stochastik
Date10. July 2015, 14:00
AbstractWe discuss uniform convergence of distribution functions in two different settings and the relation between the two. First we consider almost additive functions on lattice patterns with well defined frequencies. It is possible to embedd this context in the framework of ergodic theorems with Banach space-valued functions. If the ergodic system is generated by iid random variables it is natural to look at the same problem as an extension of the classical Glivenko-Cantelli Theorem.

 

TitleUncertainty relations and Wegner estimates for random breather potentials
InstitutionIsaac Newton Institue, Cambridge
OccasionWorkshop: Periodic and Other Ergodic Problems
Date23. March 2015, 11:30 - 12:30
Co-authorsIvica Nakic (Zagreb University), Matthias Täufer (TU Chemnitz), Martin Tautenhahn (TU Chemnitz)
AbstractWe present a new scale-free, quantitative unique continuation estimate for Schroedinger operators in multidimensional space. Depending on the context such estimates are sometimes called uncertainty relations, observations inequalities or spectral inequalities. To illustrate its power we prove a Wegner estimate for Schroedinger operators with random breather potentials. Here we encounter a non-linear dependence on the random coupling constants, preventing the use of standard perturbation theory. The proofs rely on an analysis of the level sets of the random potential, and can be extended to a rather general framework.

 

TitleUncertainty principles and spectral analysis of Schroedinger operators
InstitutionIsaac Newton Institue, Cambridge
OccasionSeminar Programme on Periodic and Ergodic Spectral Problems
Date12. March 2015

 

TitleReconstruction and estimation of rigid functions based on local data
InstitutionDurham University
OccasionGeometry and Topology Seminar
Date9. March 2015
AbstractIn many areas of mathematics and its application in other sciences one is confronted with the task of estimating or recosntruction a function based on partial data. Of course, this will not work for all functions well. Thus one needs an restriction to an adequate class of functions. This can be mathematically modeled in many ways. Spacial statistics or complex function theory are relevant areas of mathematics which come to ones mind. We present several results on reconstrucion and estimation of functions which are solutions of elliptic partial differential equations on some subset of Euclidean space. We comment also on analogous statements for solutions of finite difference equations on graphs.

 

TitleQuantitative Unique continuation estimates and Wegner bounds for random Schroedinger operators
InstitutionDepartment of Mathematics, Bristol University
OccasionMathematical Physics Seminar
Date27. February 2015

 

TitleCompressed Sensing and Sparse Recovery II
InstitutionTU Chemnitz
OccasionForschungsseminar Analysis
Date14. January 2015, 15:30

 

2014

TitleCompressed Sensing and Sparse Recovery I
InstitutionTU Chemnitz
OccasionForschungsseminar Analysis, Stochastik und Mathematische Physik
Date16. December 2014, 17:00

 

TitleMini-Course: Harmonic Analysis and Random Schrödinger Operators
InstitutionFacultad de Matemáticas, Pontificia Universidad Católica de Chile
Date13. November - 21. November 2014

 

TitleQuantitative unique continuation estimate and Wegner estimate for the standard random breather potential
InstitutionPontificia Universidad Catolica de Chile
OccasionEinladung zum Plenarvortrag bei der International Conference Spectral Theory and Mathematical Physics
DateNovember 2014
AbstractWe present a new scale-free, quantitative unique continuation estimate for Schroedinger operators in multidimensional space. Depending on the context such estimates are sometimes called uncertainty relations, observations inequalities or spectral inequalities. To illustrate its power we prove a Wegner estimate for Schroedinger operators with random breather potentials. Here we encounter a non-linear dependence on the random coupling constants, preventing the use of standard perturbation theory. The proofs rely on an analysis of the level sets of the random potential, and can be extended to a rather general framework.

 

TitleUnique countinuation principles, uncertainty relations and observability estimates for elliptic equations with multiscale structure
InstitutionEcole des Ponts Paristech
Date28. October 2014
AbstractWe consider Schroedinger operators and related elliptic partial differential equations. Domains are large cubes in Euclidean space. We are aiming for estimates which are independent of the size of the cube, since we want to pass to the thermodynamic limit. We derive scale-free quantitative unique continuation principles for eigenfunctions, and for linear combinations thereof. They can be formulated, respectively interpreted, as uncertainty relations, observability estimates, or spectral inequalities. We indicate the applicability of these estimates in various areas of analysis of PDE.

 

TitleScale-free uncertainty principles and Wegner estimates for random breather potentials
InstitutionUniversität Paris 6
OccasionSeminar
Date27. October 2014, 14:30

 

TitleUncertainty principles applied to observation and reconstruction of functions
InstitutionUniversität Jena
OccasionEinladung zum Plenarvortrag beim meeting Mathematical Physics in Jena
Date17. September 2014
AbstractIn several areas of mathematics appears the task of reconstructing, or at least estimating, a function on the basis of partial data. Often the partial data contain in formation about the Fourier transform as well as about the function itself. In this case the reconstruction or observation can be facilitated by various forms of the uncertainty principle. We discuss several classical as well as recent instances of such re sults. Thereafter we focus on the case of solutions of partial differential equations, where the uncertainty relation takes the form of a unique continuation estimate. Finally, we formulare two recently obtaied results, and discuss their application to con trol theory, perturbation of eigenvalues, and random Schrödinger operators.

 

TitleUncertainty principles applied to observation and reconstruction of functions
InstitutionTU Chemnitz
OccasionChemnitz-Zagreb Workshop on Harmonic Analysis for PDE, Applications, and related topics
Date1. July 2014, 10:00

 

TitleUncertainty and unique continuation principles for the observation of eigenfunctions
InstitutionUniversität Jena
OccasionOberseminar Analysis, Geometrie und Stochastik
Date18. June 2014, 17:00

 

TitleGrenzverteilungssäatze für stochastische Modelle komplexer physikalischer Systeme
InstitutionUniversität Jena
OccasionStochastisches Kolloquium
DateJune 2014

 

TitleGrenzverteilungssätze für Modelle ungeordneter Systeme
InstitutionUniversität zu Köln
OccasionWorkshop Stochastik
DateJanuary 2014

 

TitleEigenwert-Statistiken und -Verteilungsfunktionen
InstitutionFern-Universität Hagen
OccasionOberseminar Stochastik
DateJanuary 2014

 

TitleEigenwert-Statistiken und -Verteilungsfunktionen
InstitutionUniversität Wuppertal
OccasionOberseminar Stochastik
Date22. January 2014, 15:00
AbstractDer Vortrag diskutiert Gesetze der Grossen Zahlen fuer Zufallsvariablen mit Werten in einem Funktionenraum. Dies wird genutzt um die spektrale Vertelungsfunktion (Integrierte Zusantdsdichte) als uniformen Limes von normierten Eigenwertzaehlfunktionen zu definieren. Wir gehen auf asymptotische Eigenschaften der spektralen Vertelungsfunktion ein. Daraufhin betrachten wir geeigent reskalierte Eigenwerte und zeigen, dass in gewissen Regimen die entsprechnden Punktprozesse gegen einen Poissonprozess konvergieren.

 

TitleUnique continuation and equidistribution properties for eigenfunctions of elliptic operators
InstitutionUniversität Bonn
OccasionSeminar Stochastic and Geometric Analysis
DateJanuary 2014, 10:00

 

2013

TitleMultiscale unique continuation properties of eigenfunctions
InstitutionUniversität Zagreb
OccasionNumerical Analysis Seminar
DateOctober 2013

 

TitleEquidistribution properties of eigenfunctions and solutions of PDE
InstitutionHumboldt University of Berlin
OccasionQMath12
Date12. September 2013, 10:30

 

TitleIntegralabschätzungen für Eigenfunktionen auf multiplen Skalen
InstitutionTU Chemnitz
OccasionForschungsseminar Harmonische Analysis
DateJuly 2013

 

TitleEquidistribution properties of eigenfunctions and solutions
OccasionSymposium Operator Semi-groups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics
Date3. June 2013, 14:30

 

TitleAlloy potentials on the lattice: (absence of ) monotonicity, regularity, and spectral averages
InstitutionFernUniversität in Hagen
OccasionConference Mathematical Physics of Disordered Systems - A Conference in Honor of Leonid Pastur
Date17. May 2013, 10:05

 

2012

TitleEquidistribution properties of PDE-eigenfunctions
InstitutionInstitute of Mathematics of Bordeaux, University Bordeaux 1
OccasionConference Spectral Theory and Its Applications
Date4. October 2012, 09:00
AbstractIn a joint paper with C. Rojas-Molina we have proven that eigenfunctions of the time-independent Schrödinger-equation on large cubes (with Dirichlet or periodic b.c.) exhibit a type of quantitative equidistribution property, which is uniformly good over arbitrary lenght scales. We present this result and discuss applications, extensions and open problems.

 

TitleEquidistribution properties of eigenfunctions of PDEs
InstitutionJohannes Gutenberg-Universität Mainz
OccasionTrilateral German-French-Russian Workshop on Asymptotic analysis and spectral theory on non-compact structures
DateSeptember 2012

 

TitleDiskussion über das Zusammenspiel von Bewegung und Zufall anhand von Beispielen
InstitutionTU Chemnitz, Professur Stochastik
OccasionTag der offenen Tür, Studieninfos & Specials
Date9. June 2012, 14:00

 

TitleGleichverteilungseigenschaften von Lösungen von PDEs
InstitutionTU Bergakademie Freiberg, Institut für Numerische Mathematik und Optimierung
OccasionSeminar
Date8. June 2012, 11:00

 

TitleStochastische und Geometrische Aspekte in der Spektraltheorie zufälliger Operatoren
InstitutionTU Chemnitz
OccasionJoint workshop of the departments of Mathematics and Informatics
DateJune 2012

 

TitleGlivenko-Cantelli-Theorems, concentration inequalities, and the IDS
InstitutionInstitut de Mathématiques de Jussieu, Université Paris 13
OccasionConference: Mathématiques des systémes quantiques désordonnés
Date29. May 2012, 10:50
AbstractThe Glivenko-Cantelli Theorem states that the distribution functions of empirical measures generated by real-valued iid samples converge uniformly to the distribution function of the original measure. There exist various extensions of the Theorem to the mutivariate case and to Banach-space random variables, as well as criteria when the convergence holds in a stronger topology. We discuss the relation of the above results to concentration inequalities and applications in the spectral theory of random operators.

 

TitleAnwendungen des Satzes von Glivenko-Cantelli
InstitutionUniversität Jena, Lehrstuhl für Analysis
OccasionOberseminar Analysis, Geometrie und Stochastik
Date11. May 2012, 11:15

 

TitleEigenschaften von Lösungen von partiellen Differentialgleichungen
InstitutionTeschnische Universität Ilmenau, Institut für Mathematik
OccasionMathematisches Kolloquium
Date10. May 2012, 17:00

 

TitleScale-uniform quantitative unique continuation principle
InstitutionFAU Erlangen-Nürnberg, Department Mathematik
OccasionSeminar Mathematische Physik
Date22. March 2012, 10:30

 

TitleScale-uniform quantitative unique continuation principle
InstitutionTU Graz, Institut für numerische Mathematik
OccasionSeminar Angewandte Analysis und Numerische Mathematik
Date19. March 2012, 11:00

 

TitleUncertainty relation: applications and methods
InstitutionUniversität Zagreb, Institut für Mathematik
OccasionSeminar Numerische Mathematik und Wissenschaftliches Rechnen
Date15. March 2012

 

TitleSpectral averaging in the mathematical theory of Anderson localization
InstitutionUniversität Zagreb, Institut für Physik
OccasionSeminar des Instituts für Physik
Date14. March 2012

 

TitleScale-uniform quantitative unique continuation principle
InstitutionUniversität Zagreb, Institut für Mathematik
OccasionColloquium
Date13. March 2012

 

TitleSkaleninvariantes quantitatives Eindeutiges-Fortsetzungsprinzip und Anwendungen
InstitutionSeminar Analysis, TU Dresden
OccasionAnalysis Seminar
Date19. January 2012

 

2011

TitleScale-free quantitative unique continuation principle
InstitutionMax-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig
OccasionAnalysis Seminar
Date15. December 2011

 

TitleLow lying spectrum of randomly perturbed periodic waveguides
InstitutionDoppler Institute in Department of Theoretical Physics of the Nuclear Physics Institute, Rez
OccasionSeminar
Date18. November 2011

 

TitleUnique continuation principle and Wegner estimates
InstitutionMathematisches Forschungsinstitut Oberwolfach
OccasionWorkshop "Correlations and Interactions for Random Quantum Systems"
Date24. October 2011

 

TitleUnique continuation properties of solutions of elliptic second order differential equations (1) and (2)
InstitutionTU Chemnitz
OccasionSeminar "Partielle Differentialgleichungen und Inverse Probleme"
Date21. October 2011 and 11. November 2011
AbstractBei vielen Typen von (partiellen) Differentialgleichungen ist bekannt, dass einen nichttriviale Lösung nicht auf einer offenen Menge verschwinden kann. Diese Eigenschaft wird im Englischen "unique continuation property" genannt. Oftmals wird sie aus einer Carleman-Ungleichung hergeleitet. Ein wichtiger Anwendungsberich ist die Eindeutigkeit der Lösung von nichtlinearen Differentialgleichungen. In manchen Situationen ist es von Interesse, eine quantitative Version der "unique continuation property" herzuleiten. Wir diskutieren dies.

 

TitleDynamics and spectra of the Schrödinger equation
InstitutionMathematical Society in Split
OccasionColloquium
Date21. September 2011

 

TitleEigenvalue flows for operator-pencils
InstitutionSveučilište u Splitu, Fakultet elektrotehnike, strojarstva i brodogradnje
OccasionMathematics seminar
Date20. September 2011

 

TitleEigenvalue flows for linear pencils of operators
InstitutionHotel Colentum
OccasionWorkshop on quantitative spectral theory and mathematical physics
Date16. September 2011

 

TitleLocalisation, Lifschitz tails and Wegner estimates for random Schrödinger operators
InstitutionInstitut de Mathématiques de Bordeaux
OccasionSeminar Equipe Analyse
Date8. September 2011

 

TitleZufällige Schrödingeroperatoren mit nicht-monotoner Parameter-Abhängigkeit
InstitutionJohannes Gutenberg-Universität Mainz
Date28. January 2011

 

2010

TitleGeometrische und Spektrale Eigenschaften von Perkolationsclustern auf Cayleygraphen
InstitutionKarlsruher Institut für Technologie
Date16. November 2010

 

TitleSpectral properties of random Schroedinger operators with general interactions
InstitutionPontificia Universidad Catolica de Chile
OccasionSeminar on Partial Differential Equations and Spectral Theory
Date30. September 2010

 

TitleSpectral properties and averaging for discrete alloy type potentials
InstitutionPontificia Universidad Catolica de Chile
OccasionPlenary talk at the International Conference "Spectral Days"
Date21. September 2010

 

TitleFractional moment method for non-monotone models
InstitutionUniversity of Hradec Kralove
OccasionQMath11 Mathematical Results in Quantum Physics, Hradec Kralove
Date6. September 2010

 

TitleDiscrete alloy type models: averaging and spectral properties
InstitutionIsaac Newton Institute for Mathematical Sciences, Cambridge, UK
OccasionInvited talk at the workshop "Analysis on Graphs and its Applications Follow-up meeting"
Date29. July 2010

 

TitleSpectral distribution function of percolation operators
VenueDepartment Mathematik, Universität Erlangen-Nürnberg
OccasionAG Mathematische Physik
Date17. June 2010

 

2009

TitleDiscrete alloy type models with single site potentials of changing sign
VenueClarion Congress Hotel Prague
OccasionInternational Congress on Mathematical Physics, Invited talk in the section on Nonrelativistic Quantum Mechanics
Date4. August 2009

 

TitleGeometrische und Spektrale Eigenschaften von Perkolationsclustern auf Cayleygraphen
InstitutionUniversität Mainz
Occasionjob application talk
Date16. July 2009

 

TitleExponentieller Abfall der Greenschen Funktion für Legierungsmodelle auf $\Bbb Z$
InstitutionUniversität Oldenburg
Date10. July 2009

 

TitlePercolation clusters on Calyey graphs and their spectra
Occasion"Alp-Workshop", St.~Kathrein am Offenegg bei Graz
Date5. July 2009

 

TitleSpektrale Eigenschaften von diskreten Legierungsmodellen
InstitutionRuhr-Universität Bochum
OccasionOberseminar über Mathematische Physik
Date1. July 2009

 

TitleExponential decay of Green's function for Anderson models on $\Bbb Z$ with single-site potentials of finite support
InstitutionUniversität Mainz
OccasionOberseminar Analysis
Date30. June 2009

 

TitleGeometric and spectral properties of percolation on Cayley graphs
InstitutionUniversität Paderborn
Occasionjob application talk
Date3. April 2009

 

TitleBounds on the spectral shift function and applications
InstitutionDurham University
OccasionPure Mathematics Colloquium
Date16. March 2009

 

TitlePercolation clusters on Calyey graphs and their spectra
InstitutionImperial College
OccasionLondon Analysis and Probability Seminar
Date12. March 2009

 

TitleBounds on the spectral shift function and applications
InstitutionUniversity College London
OccasionMathematics Seminar
Date11. March 2009

 

TitleGeometric and spectral properties of percolation on Cayley graphs
InstitutionUniversity of Bristol
OccasionAnalysis Seminar
Date9. March 2009

 

2008

TitleGeometrische und spektrale Eigenschaften von Perkolationgraphen
InstitutionInstitut für Mathematik, TU Berlin
Occasionjob application talk
Date17. December 2008

 

TitlePerkolationscluster auf Cayleygraphen und deren Spektren
InstitutionFaculty of Mathematics, TU Cemnitz
Occasionjob application talk
Date12. December 2008

 

TitlePercolation and spectra on Cayley-graphs
OccasionOberwolfach-Workshop "Interplay of Analysis and Probability in Physics"
Date2. December 2008

 

TitleGeometrische und spektrale Eigenschaften von Perkolationgraphen
InstitutionTU Chemnitz
OccasionForschungsseminar Alogrithmische und Diskrete Mathematik
Date26. November 2008

 

TitleBounds on singular values of semigroup differences and the spectral shift function
InstitutionTU Clausthal
OccasionMathematisches Kolloquium
Date19. November 2008

 

TitleGeometrische und spektrale Aspekte von Perkolation auf allgemeinen Graphen
InstitutionFakultät für Mathematik und Informatik, Universität Bremen
Occasionjob application talk
Date18. November 2008

 

TitlePerkolation auf homogenen Graphen
InstitutionFakultät für Mathematik und Informatik, Fern-Universität Hagen
Occasionjob application talk
Date24. October 2008

 

TitleGeometrische und spektrale Eigenschaften von Perkolationteilgraphen
InstitutionTU Dortmund
OccasionOberseminar Geometrie
Date23. October 2008

 

TitlePerkolation auf homogenen Graphen
InstitutionSchool of Mathematics and Computer Science, Friedrich-Schiller-Universität of Jena
Occasionjob application talk
Date7. October 2008

 

TitleClassical and Quantum percolation
InstitutionInstitut für Mathematik C, Technische Universität Graz
Date28. July 2008

 

TitleSingular values of semigroup differences and applications to the spectral shift function
InstitutionTU Berlin
Date24. July 2008

 

TitleGeometrische und spektrale Eigenschaften von Perkolation auf Cayleygraphen
InstitutionUniversität Tübingen
Occasionjob application talk
Date15. July 2008

 

TitlePercolation on Cayley and quasi-transitive graphs
InstitutionUniversität Bielefeld
OccasionWorkshop des SFB 701 "Aspects of Aperiodic Order"
Date4. July 2008

 

TitleGeometrische und spektrale Eigenschaften von Perkolation auf Cayleygraphen
InstitutionRuhr-Universität Bochum
Occasionjob application talk
Date1. July 2008

 

TitleEstimates on singular values and the spectral shift function, with applications
InstitutionUniversität Bielefeld
Occasionjob application talk
Date26. June 2008

 

TitleSpectral and geometric properties of percolation on general graphs
OccasionESF-Conference "Operator Theory, Analysis and Mathematical Physics", Bedlewo, Polen
Date16. June 2008

 

TitleSpectral and geometric properties of percolation on general graphs
InstitutionInstitut für Mathematik, TU Clausthal
OccasionMathematisches Kolloquium
Date28. May 2008

 

TitleSpectral and geometric properties of percolation on general graphs
InstitutionInstitut for Theoretical Physics, Universität Hamburg
OccasionSeminarreihe "Quantum Field Theory and Mathematical Physics"
Date27. May 2008

 

TitleIntegrated density of states for Schrödinger operators on metric graphs
InstitutionHumboldt Universiy of Berlin
OccasionWorkshop "Mathematical Physics and Spectral Theory"
Date25. April 2008

 

TitleWegner estimates for non-monotoneously correlated alloy type models
OccasionOberwolfach-Workshop, Disordered Systems: Random Schrödinger Operators and Random Matrices
Date25. March 2008

 

TitleOn spectral properties of correlated and non-monotone Anderson models
OccasionGerman Open Conference on Probability and Statistics, Aachener Stochastiktage
Date6. March 2008

 

TitleSpectral and geometric properties of percolation on general graphs
InstitutionUniversität Bielefeld
OccasionSeminar des SFB 701
Date23. January 2008

 

2007

TitleLow energy asymptotics of percolation Laplacians on Cayley graphs
InstitutionHausdorff-Institut, Bonn
OccasionWorkshop "Particle systems, nonlinear diffusions, and equilibration"
Date15. November 2007

 

TitlePerkolationsprozesse und Laplaceoperatoren auf Cayleygraphen
InstitutionPhilipps-Universität Marburg
OccasionKolloquium des Fachbereichs Mathematik und Informatik
Date15. August 2007

 

TitleLow energy asymptotics of percolation Hamiltonians on graphs
InstitutionTU Wien
OccasionConference "Equadiff 07"
Date6. August 2007

 

TitleSpectral asymptotics of percolation Laplacians on amenable Cayley graphs
InstitutionIsaac Newton Institute
OccasionWorkshop on "Quantum Graphs, Their Spectra and Applications"
Date3. April 2007

 

TitleLifshitz tails for random Hamiltonians monotone in the randomness
OccasionOberwolfach Mini-Workshop "Multiscale and variational methods in materials science and the quantum theory of solids"
Date12. February 2007

 

2006

TitleUntere Schranken an Eigenwertabstände
OccasionChemnitzer Mathematisches Colloquium
Date7. December 2006

 

TitleLifshitz tails for the IDS of Schrödinger operators with random breather-type potential
OccasionInternational Conference "Operator Theory in Quantum Physics", Prag
Date28. September 2006

 

TitleLifshitz tails for Schrödinger operators with random breather-type potential
OccasionConference "Operator Theory, Analysis and Mathematical Physics", Lund
Date16. June 2006

 

TitleExistenz- und Stetigkeitseigenschaften der Integrierten Zustandsdichte
OccasionChemnitzer Mathematisches Colloquium
Date18. May 2006

 

TitleAnderson-percolation Hamiltonians and compactly supported eigenstates
OccasionInterdisciplinary Workshop "Evolution on Networks", Blaubeuren
Date1. May 2006

 

TitleUntere Schranken an die unterste spektrale L¨cke von Hamiltonoperatoren mit singulärem Potential
InstitutionRWTH Aachen
OccasionSeminar des Graduiertenkollegs "Hierarchie und Symmetrie in mathematischen Modellen"
Date24. April 2006

 

TitleAnderson-percolation Hamiltonians and compactly supported eigenstates
InstitutionTU Graz
OccasionStrukturtheorie-Seminar
Date20. April 2006

 

TitleSpectral analysis of percolation Hamiltonians
OccasionOberwolfach Mini-Workshop on "$L^2$-Spectral Invariants and the Integrated Density of States"
Date24. February 2006

 

TitleTiefliegendes Spektrum von zufälligen Schrödingeroperatoren
InstitutionTU Chemnitz
OccasionForschungsseminar Algorithmische und Diskrete Mathematik
Date25. January 2006

 

TitleSpectral properties of Anderson-percolation Hamiltonians on graphs
InstitutionErwin Schrödinger Institut, Wien
OccasionWorkshop "Aspects of Spectral Theory"
Date19. January 2006

 

TitleCompactly supported eigenfunctions of Hamiltonians on infinite graphs and jumps of the IDS
InstitutionUniversität Bielefeld
OccasionSeminar des SFB 701
Date4. January 2006

 

2005

TitleUntere Schranken an die unterste spektrale Lücke von Hamiltonoperatoren mit singulärem Potential
InstitutionUniversity Osijek, Croatia
Date19. December 2005

 

TitleLower bounds on the lowest spectral gap of singular potential Hamiltonians
InstitutionUniversität Bonn
OccasionSymposium "Dirichlet Forms, Stochastic Analysis and Interacting Systems"
Date24. November 2005

 

TitleLower bounds on the lowest spectral gap of singular potential Hamiltonians
InstitutionUniversité de Cergy-Pontoise, France
Date28. September 2005

 

TitleSpectral Analysis of Percolation Hamiltonians
OccasionWorkshop "Computation and Analytic Problems in Spectral Theory", Gregynog, Wales
Date28. July 2005

 

TitleBounds on the spectral shift function and the density of states
InstitutionMax-Plank-Institut, Leipzig, Germany
Date24. May 2005

 

TitleLocalization for alloy-type models: rigorosus results and methods
InstitutionDepartment of Physics, Chemnitz
Date13. April 2005

 

TitleSpectral analysis of percolation Hamiltonians
InstitutionUniversité Paris, France
Date8. March 2005

 

TitleQuantenmechanik ungeordneter Festkörper: das Phänomen der Lokalisierung
OccasionKolloquium der Kroatischen Mathematischen Gesellschaft, Zagreb
Date23. February 2005

 

TitleSpectral properties of periodic and random Schrödinger operators
InstitutionUniversity of Bath, UK
Date14. February 2005

 

TitleSpectral properties of the quantum percolation model on graphs
InstitutionUniversity of Durham, UK
Date9. February 2005

 

2004

TitleBounds on the spectral shift function and the density of states
InstitutionTU Dresden
DateNovember 2004

 

TitleSpektren von Quantenperkolationsmodellen
InstitutionUniversität Augsburg
Date22. November 2004

 

TitleSpectral averaging induced by random, geometric perturbations
InstitutionDoppler Institute, Prag
DateNovember 2004

 

TitleSpectral Analysis of Percolation Hamiltonians
OccasionQMath-9: Mathematical Results in Quantum Mechanics, Giens
DateSeptember 2004

 

TitleBounds on the spectral shift function and the density of states
OccasionMathematics and Physics of Disordered Systems, Oberwolfach
DateMay 2004

 

TitleSpektrale Verschiebung induziert durch ein kompakt getragenes Potential
InstitutionSymposium über Analysis, Universitäat Basel
DateApril 2004

 

TitleIntegrated density of states for random metrics on manifolds
InstitutionCity University of New York
DateFebruary 2004

 

2003

TitleSpectral properties of the quantum percolation model on graphs
InstitutionRuhr-Universität Bochum
DateDecember 2003

 

TitleSpectral shift induced by a compactly supported potential
InstitutionUniversität Mainz
DateDecember 2003

 

TitleSpectral shift induced by a compactly supported potential
InstitutionUniversität Stuttgart
DateNovember 2003

 

TitleSpectral shift induced by a compactly supported potential
InstitutionUniversität Konstanz
DateNovember 2003

 

TitleSpectral shift induced by a compactly supported potential
InstitutionUniversity of Alabama at Birmingham
DateOctober 2003

 

TitleSpectral shift induced by a compactly supported potential
OccasionCalTech
DateOctober 2003

 

TitleSpectral shift induced by a compactly supported potential
InstitutionTU Chemnitz
DateJuly 2003

 

TitleSpectral shift induced by a compactly supported potential
InstitutionRuhr-Universität Bochum
DateJuly 2003

 

TitleSpectral shift induced by a compactly supported potential
InstitutionUniversity Zagreb
DateJuly 2003

 

TitleSpectral properties of quantum percolation models
OccasionConference Applied Mathematics and Scientific Computing, Brijuni, Kroatien
Date25. June 2003

 

TitleSpectral properties of the quantum percolation model on graphs
OccasionCalTech
DateMarch 2003

 

TitleWegner estimates for indefinite potentials and inverses of Toeplitz matrices
OccasionWestern States Mathematical Physics Meeting, CalTech
DateFebruary 2003

 

2002

TitleOn Wegner estimates with singular and indefinite randomness
InstitutionUC Irvine
Date12. December 2002

 

TitleIntegrated density of states for random metrics on manifolds
OccasionCalTech
DateNovember 2002

 

TitleIntegrated density of states for random metrics on manifolds
InstitutionRuhr-Universität Bochum
DateOctober 2002

 

TitleExistence of the density of states for single site potentials with samll support in one dimension
OccasionWorkshop Between Order and Disorder, Greifswald
DateSeptember 2002

 

TitleWegner estimate with local continuity requirements on the coupling constants
OccasionConference on Differential Equations and Mathematical Physics, Birmingham, USA
Date26. March 2002

 

TitleLokalisierung an Floquet-regulären Bandkanten
InstitutionInstitut für Theoretische Physik I, Universität Erlangen-Nürnberg
DateJanuary 2002

 

TitleGruppoide von Neumann Algebren und die Integrierte Zustandsdichte
InstitutionInstitut für Theoretische Physik I, Universität Erlangen-Nürnberg
DateJanuary 2002

 

TitleExistenz der Zustandsdichte für indefinite Legierungspotentiale
InstitutionFakultät für Mathematik, TU Chemnitz
DateJanuary 2002

 

2001

TitleLipschitz continuity of integrated density of states for single site potentials with small support
OccasionMathematical results in Quantum Mechanics, Taxco, Mexico
DateDecember 2001

 

TitleIntegrated density of states for random operators on manifolds
OccasionWorkshop Schrödinger Operators, IIMAS, UNA Mexico
Date7. December 2001

 

TitleWegner estimate for sparse and other generalized alloy type potentials
OccasionWorkshop Schrödinger Operators, IIMAS, UNA Mexico
Date5. December 2001

 

TitleThe integrated Density of states and Wegner estimates
OccasionWorkshop Schrödinger Operators, IIMAS, UNA Mexico
Date3. December 2001

 

TitleExistence of the density of states for Anderson models with indefinite single site potentials
OccasionWorkshop SFB 237, Tutzing
DateOctober 2001

 

TitleIntegrated Density of states for random Schrödinger Operators on manifolds
OccasionMini-Conference Random Schrödinger Operators, Tsukuba, Japan
DateAugust 2001

 

TitleWegner Estimate for Indefinite Anderson Potentials
InstitutionResearch Institute for Mathematical Sciences, Kyoto
OccasionWorkshop Applications of Renormalization Group Methods in Mathematical Sciences
DateJuly 2001

 

TitleWegner estimates for alloy type potentials with changing sign
InstitutionUniversity of Osaka
DateJuly 2001

 

TitleLocalization by disorder at Floquet-regular spectral boundaries
InstitutionUniversity of Osaka
DateJuly 2001

 

TitleRegularity porperties of the integrated density of states of random Schrödinger operators
OccasionConference Applied Mathematics and Scientific Computing, Dubrovnik, Croatia
DateJune 2001

 

TitleDie Wegner-Abschätzung und die gemeinsame Dichte der Anderson-Kopplungskonstanten
OccasionConference Schrödinger Operators, Oberwolfach
DateJune 2001

 

TitleSpektrale Eigenschaften von periodischen und zufälligen Schrödingeroperatoren
InstitutionUniversity Zagreb, Croatia
DateMay 2001

 

TitleWegner estimates for alloy type potentials with changing sign
OccasionSchrödinger operators, Oberwolfach
DateMay 2001

 

TitleSpektrale Eigenschaften von zufälligen Schrödingeroperatoren
InstitutionFern-Universität Hagen
DateMarch 2001

 

2000

TitleWegner Abschätzung für indefinite, überlappende Anderson Potentiale mit glatter Dichte
OccasionAG Mathematische Physik, Bochum
Date5. October 2000

 

TitleWegner Abschätzung für indefinite, überlappende Einzelpotentiale mit glatter Dichte
OccasionWorkshop "Ungeordnete Systeme", Bochum
DateMay 2000

 

TitleIntegrated density of states for Schrödinger operators on manifolds
OccasionConference on Differential Geometry and Quantum Physics, Berlin
DateMay 2000

 

TitleIntegrated density of states for Schrödinger operators on manifolds
OccasionInstitut für Angewandte Mathematik, Universität Bonn
DateJanuary 2000

 

1999

TitleWegner Abschätzung für indefinite Anderson-Potentiale
OccasionWorkshop SFB 237, Bad Honnef
DateSeptember 1999

 

TitleWegner estimates for alloy type potentials with changing sign
InstitutionUniversity of Lulea, Sweden
DateSeptember 1999

 

TitleWegner estimate for the Anderson model with indefinite potential
InstitutionNTNU Trondheim, Norway
DateAugust 1999

 

TitleWegner estimate for the Anderson model with indefinite potential
OccasionConference on Differential Equations and Mathematical Physics, Birmingham, USA
DateMay 1999

 

1998

TitleRandom potentials causing localisation
OccasionWorkshop SFB 237, Bad Honnef
DateSeptember 1998

 

Kontakt

Adresse

TU Dortmund
Fakultät für Mathematik
Lehrstuhl IX
Vogelpothsweg 87
44227 Dortmund

Sie finden uns auf dem sechsten Stock des Mathetowers.

Sekretariat

Janine Textor (Raum M 620)

Tel.: (0231) 755-3063
Fax: (0231) 755-5219
Mail: janine.textor@tu-dortmund.de

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