# Prof. Dr. Ivan Veselić - Talks

### 2020

Title Uncertainty relations, control theory and perturbation of spectral bands Department of Mathematical Sciences, University of Durham, England Analysis and/of PDE Seminar 5. November 2020, 15:00 CET Slides of the talk are provided here.

Title Quantitative unique continuation estimates and resulting uncertainty relations for Schroedinger and divergence type operators Department of Mathematical Sciences, University of Bath Research seminar: Asymptotics, operators, and functionals 12. October 2020, 17:15-19:45 CEST The 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.

Title Scale-free uncertainty relations and applications in spectral and control theory Brijuni, Croatia Tenth Conference on Applied Mathematics and Scientific Computing 15. September 2020 We 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.

Title Scale-free uncertainty relations for spectral projectors and applications Institut für Mathematik der Humboldt-Universität zu Berlin Workshop: Analytical Modeling and Approximation Methods 5. March 2020

### 2019

Title Upper and lower Lipschitz bounds for shifting the edges of the essential spectrum of Schroedinger operators Université Côte d'Azur / Laboratoire Mathématiques & Interactions J.A. Dieudonné Séminaire de l'équipe EDP Analyse Numérique 28. November 2019 The 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.

Title Upper and lower Lipschitz bounds for perturbation of the edges of the essential spectrum Sveučilište u Dubrovniku Seminar za primijenjenu matematiku i teoriju upravljanja 29. August 2019 Periodic 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.

Title Spectral inequalities and null control for the heat conduction problem on domains with multiscale structure Universität Bonn 5. July 2019 I 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.

Title Uncertainty relations and null control for the heat conduction problem on domains with multiscale structure Fern-Universität Hagen Conference "On mathematical aspects of interacting systems in low dimension" 24. June - 27. June 2019 I 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.

Title Upper and lower Lipschitz bounds for perturbation of the edges of the essential spectrum Fern-Universität Hagen Oberseminar Mathematische Physik 2. April 2019

Title Null-controllability of the heat equation on bounded and unbounded domains TU Dortmund Oberseminar Numerische Analysis und Optimierung 14. March 2019

### 2018

Title Wegner estimate for Landau-breather Hamiltonians Pontificia Universidad Catolica de Chile Spectral Theory and PDE Seminar 13. December 2018 I 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.

Title Scale free unique continuation estimates with three applications Pontificia Universidad Catolica de Chile International Conference "Spectral Theory and Mathematical Physics 2018" 06. December 2018 I 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.

Title Uncertainty principles and null-controllability of the heat equation on bounded and unbounded domains University of Split ApplMath18 Ninth Conference on Applied Mathematics and Scientific Computing, Solaris, Sibenik, Croatia 17. September - 20. September 2018 In 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.

Title Null controllability for the heat equation University of Split Splitsko matematicko drustvo 14. September 2018 In 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.

Title Upper and lower Lipschitz bounds for the perturbation of edges of the essential spectrum Universitaet Bielefeld Kolloquium Mathematische Physik 01. June 2018 Let 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.

Title Uniform Approximation of the integrated density of states on amenable groups Bergische Universitaet Wuppertal Workshop Ergodic Theory 05. May 2018

Title Necessary and sufficient geometric condition for null-controllability of the heat equation on $\Bbb R^d$. Fernuni Hagen Workshop on "Control theory of infinite-dimensional systems" 10. January - 12. January 2018 In 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

Title Glivenko Cantelli and Ergodic Theorem on groups. Ruhr Uni Bochum (RUB) RTG 2131-Seminar 23. October 2017

Title Glivenko Cantelli and Banach-space ergodic theorems applied to the uniform approximation of the integrated density of states Universität Trier French-German meeting Aspect 17: Asymptotic Analysis and Spectral Theory 25. September - 29. September 2017 The 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.)

Title Glivenko-Cantelli Theory, Banach-space valued Ergodic Theorems and uniform approximation of the integrated density of states Universität Potsdam International Conference on Analysis and Geometry on Graphs and Manifolds 31. July - 04. August 2017 The 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.)

Title Unique continuation estimates and lifting of eigenvalues. Euler Institute, Saint-Petersburg, Russia 9th Birman Conference in Spectral Theory 03. July - 06. July 2017 Using 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.

Title Dichotomy for the expansion of the deterministic spectrum of random Schroedinger operators Bergische Universität Wuppertal Hagen-Wuppertal Analysis-Treffen 2. May 2017

Title Unique continuation estimates and the Logvinenko Sereda Theorem. Fernuni Hagen Oberseminars Stochastik/Mathematische Physik 15. February 2017 Unique 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

Title Unique continuation estimates and the Logvinenko Sereda Theorems Universite de Strasbourg Seminaire d' Analyse 13. December 2016 Unique 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.

Title Unique continuation principle and its absence on continuum and discrete geometries Technische Universität Wien Workshop on Operator Theory and Indefinite Inner Product Spaces 12. December 2016 A 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.

Title Uncertainty relations and applications to the Schrödinger and heat conduction equations Johannes Gutenberg Universität Mainz Summer school Mainz 13. September 2016 In 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.

Title A dummies view on compressive sensing University of Split School of Medicine, Split, Croatia Summer school Split 27. August - 03. September 2016

Title Unique continuation principle and its absence on continuum space, on lattices and on quantum graphs WIAS Berlin NewMET 2016 14. July - 15. July 2016 A 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.

Title Multiscale equidistribution estimates for Schr ̈odinger eigenfunctions Department of Mathematics, Faculty of Science, University of Zagreb, Croatia International Workshop on PDEs: analysis and modelling Celebrating 80th anniversary of professor Nedžad Limić 19. June - 22. June 2016 We 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

Title Quantitative uncertainty principles in harmonic analysis and mathematical physics 6th Croatian Mathematical Congress 16. June 2016 In 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 Fern-Universität Hagen Seminar Stochastik 4. January 2016

### 2015

Title Weihnachtsvorlesung "(Miss)Verständnis der Stochastik" Technische Universität Chemnitz Weihnachtsvorlesung am Tag der Lehre 3. December 2015, 15:30 bis 17:00, Zentrales Hörsaalgebäude, Raum N112. Weihnachtsvorlesung zu Themen der Stochastik für ein breites Publikum

Title Hadamard's three line theorem and Carleman estimates (Hadamardov teorem of tri pravca i Carlemanove ocjene) Zagreb University , Mathematics department Colloquium of the Croatian Mathematical Society 30. September 2015, 17:00 We 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. http://degiorgi.math.hr/kolokvij/view.php?id=121

Title Uniform ergodic theorems and the Glivenko-Cantelli theorem (Uniformni ergodički teoremi i Glivenko Cantellijev teorem) Zagreb University , Mathematics department Probabilty seminar 29. September 2015, 14:30 https://web.math.pmf.unizg.hr/zzvs/?Seminars

Title Approximation and estimation of functions based on local data (Aproksimacija i ocjena funkcija na osnovu lokalnih podataka) Rijeka University, Department of Natural Sciences and Mathematics Colloquium of the society of mathematicians and physicists 28. September 2015, 12:00 In 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. http://dmf.hr/2015/06/19/aproksimacija-i-ocjena-funkcija-na-osnovu-lokalnih-podataka/

Title Uncertainty relations and applications (Relacije neodređenosti i primjene) University of Split Seminar of the Split mathematical society 18. September 2015, 12:00 http://www.stmath.hr/?p=654

Title Compressed sensing and the Calderon problem in electrical impedance tomography University of Split Speech and Hearing Research Lab, School of Medicine 17. September 2015, 11:00 http://kovaciclab.org/seminar-prof-dr-sc-ivan-veselic-compressed-sensing-calderon-problem-on-electrical-impedance-tomography/

Title Glivenko-Cantelli theory for almost additive functions and Banach space-valued ergodic theorems on lattices Friedrich-Alexander-Universität Erlangen-Nürnberg Tag der Stochastik 10. July 2015, 14:00 We 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.

Title Uncertainty relations and Wegner estimates for random breather potentials Isaac Newton Institue, Cambridge Workshop: Periodic and Other Ergodic Problems 23. March 2015, 11:30 - 12:30 Ivica Nakic (Zagreb University), Matthias Täufer (TU Chemnitz), Martin Tautenhahn (TU Chemnitz) We 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.

Title Uncertainty principles and spectral analysis of Schroedinger operators Isaac Newton Institue, Cambridge Seminar Programme on Periodic and Ergodic Spectral Problems 12. March 2015

Title Reconstruction and estimation of rigid functions based on local data Durham University Geometry and Topology Seminar 9. March 2015 In 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.

Title Quantitative Unique continuation estimates and Wegner bounds for random Schroedinger operators Department of Mathematics, Bristol University Mathematical Physics Seminar 27. February 2015

Title Compressed Sensing and Sparse Recovery II TU Chemnitz Forschungsseminar Analysis 14. January 2015, 15:30

### 2014

Title Compressed Sensing and Sparse Recovery I TU Chemnitz Forschungsseminar Analysis, Stochastik und Mathematische Physik 16. December 2014, 17:00

Title Mini-Course: Harmonic Analysis and Random Schrödinger Operators Facultad de Matemáticas, Pontificia Universidad Católica de Chile 13. November - 21. November 2014

Title Quantitative unique continuation estimate and Wegner estimate for the standard random breather potential Pontificia Universidad Catolica de Chile Einladung zum Plenarvortrag bei der International Conference Spectral Theory and Mathematical Physics November 2014 We 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.

Title Unique countinuation principles, uncertainty relations and observability estimates for elliptic equations with multiscale structure Ecole des Ponts Paristech 28. October 2014 We 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.

Title Scale-free uncertainty principles and Wegner estimates for random breather potentials Universität Paris 6 Seminar 27. October 2014, 14:30

Title Uncertainty principles applied to observation and reconstruction of functions Universität Jena Einladung zum Plenarvortrag beim meeting Mathematical Physics in Jena 17. September 2014 In 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.

Title Uncertainty principles applied to observation and reconstruction of functions TU Chemnitz Chemnitz-Zagreb Workshop on Harmonic Analysis for PDE, Applications, and related topics 1. July 2014, 10:00

Title Uncertainty and unique continuation principles for the observation of eigenfunctions Universität Jena Oberseminar Analysis, Geometrie und Stochastik 18. June 2014, 17:00

Title Grenzverteilungssäatze für stochastische Modelle komplexer physikalischer Systeme Universität Jena Stochastisches Kolloquium June 2014

Title Grenzverteilungssätze für Modelle ungeordneter Systeme Universität zu Köln Workshop Stochastik January 2014

Title Eigenwert-Statistiken und -Verteilungsfunktionen Fern-Universität Hagen Oberseminar Stochastik January 2014

Title Eigenwert-Statistiken und -Verteilungsfunktionen Universität Wuppertal Oberseminar Stochastik 22. January 2014, 15:00 Der 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.

Title Unique continuation and equidistribution properties for eigenfunctions of elliptic operators Universität Bonn Seminar Stochastic and Geometric Analysis January 2014, 10:00

### 2013

Title Multiscale unique continuation properties of eigenfunctions Universität Zagreb Numerical Analysis Seminar October 2013

Title Equidistribution properties of eigenfunctions and solutions of PDE Humboldt University of Berlin QMath12 12. September 2013, 10:30

Title Integralabschätzungen für Eigenfunktionen auf multiplen Skalen TU Chemnitz Forschungsseminar Harmonische Analysis July 2013

Title Equidistribution properties of eigenfunctions and solutions Symposium Operator Semi-groups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics 3. June 2013, 14:30

Title Alloy potentials on the lattice: (absence of ) monotonicity, regularity, and spectral averages FernUniversität in Hagen Conference Mathematical Physics of Disordered Systems - A Conference in Honor of Leonid Pastur 17. May 2013, 10:05

### 2012

Title Equidistribution properties of PDE-eigenfunctions Institute of Mathematics of Bordeaux, University Bordeaux 1 Conference Spectral Theory and Its Applications 4. October 2012, 09:00 In 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.

Title Equidistribution properties of eigenfunctions of PDEs Johannes Gutenberg-Universität Mainz Trilateral German-French-Russian Workshop on Asymptotic analysis and spectral theory on non-compact structures September 2012

Title Diskussion über das Zusammenspiel von Bewegung und Zufall anhand von Beispielen TU Chemnitz, Professur Stochastik Tag der offenen Tür, Studieninfos & Specials 9. June 2012, 14:00

Title Gleichverteilungseigenschaften von Lösungen von PDEs TU Bergakademie Freiberg, Institut für Numerische Mathematik und Optimierung Seminar 8. June 2012, 11:00

Title Stochastische und Geometrische Aspekte in der Spektraltheorie zufälliger Operatoren TU Chemnitz Joint workshop of the departments of Mathematics and Informatics June 2012

Title Glivenko-Cantelli-Theorems, concentration inequalities, and the IDS Institut de Mathématiques de Jussieu, Université Paris 13 Conference: Mathématiques des systémes quantiques désordonnés 29. May 2012, 10:50 The 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.

Title Anwendungen des Satzes von Glivenko-Cantelli Universität Jena, Lehrstuhl für Analysis Oberseminar Analysis, Geometrie und Stochastik 11. May 2012, 11:15

Title Eigenschaften von Lösungen von partiellen Differentialgleichungen Teschnische Universität Ilmenau, Institut für Mathematik Mathematisches Kolloquium 10. May 2012, 17:00

Title Scale-uniform quantitative unique continuation principle FAU Erlangen-Nürnberg, Department Mathematik Seminar Mathematische Physik 22. March 2012, 10:30

Title Scale-uniform quantitative unique continuation principle TU Graz, Institut für numerische Mathematik Seminar Angewandte Analysis und Numerische Mathematik 19. March 2012, 11:00

Title Uncertainty relation: applications and methods Universität Zagreb, Institut für Mathematik Seminar Numerische Mathematik und Wissenschaftliches Rechnen 15. March 2012

Title Spectral averaging in the mathematical theory of Anderson localization Universität Zagreb, Institut für Physik Seminar des Instituts für Physik 14. March 2012

Title Scale-uniform quantitative unique continuation principle Universität Zagreb, Institut für Mathematik Colloquium 13. March 2012

Title Skaleninvariantes quantitatives Eindeutiges-Fortsetzungsprinzip und Anwendungen Seminar Analysis, TU Dresden Analysis Seminar 19. January 2012

### 2011

Title Scale-free quantitative unique continuation principle Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig Analysis Seminar 15. December 2011

Title Low lying spectrum of randomly perturbed periodic waveguides Doppler Institute in Department of Theoretical Physics of the Nuclear Physics Institute, Rez Seminar 18. November 2011

Title Unique continuation principle and Wegner estimates Mathematisches Forschungsinstitut Oberwolfach Workshop "Correlations and Interactions for Random Quantum Systems" 24. October 2011

Title Unique continuation properties of solutions of elliptic second order differential equations (1) and (2) TU Chemnitz Seminar "Partielle Differentialgleichungen und Inverse Probleme" 21. October 2011 and 11. November 2011 Bei 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.

Title Dynamics and spectra of the Schrödinger equation Mathematical Society in Split Colloquium 21. September 2011

Title Eigenvalue flows for operator-pencils Sveučilište u Splitu, Fakultet elektrotehnike, strojarstva i brodogradnje Mathematics seminar 20. September 2011

Title Eigenvalue flows for linear pencils of operators Hotel Colentum Workshop on quantitative spectral theory and mathematical physics 16. September 2011

Title Localisation, Lifschitz tails and Wegner estimates for random Schrödinger operators Institut de Mathématiques de Bordeaux Seminar Equipe Analyse 8. September 2011

Title Zufällige Schrödingeroperatoren mit nicht-monotoner Parameter-Abhängigkeit Johannes Gutenberg-Universität Mainz 28. January 2011

### 2010

Title Geometrische und Spektrale Eigenschaften von Perkolationsclustern auf Cayleygraphen Karlsruher Institut für Technologie 16. November 2010

Title Spectral properties of random Schroedinger operators with general interactions Pontificia Universidad Catolica de Chile Seminar on Partial Differential Equations and Spectral Theory 30. September 2010

Title Spectral properties and averaging for discrete alloy type potentials Pontificia Universidad Catolica de Chile Plenary talk at the International Conference "Spectral Days" 21. September 2010

Title Fractional moment method for non-monotone models University of Hradec Kralove QMath11 Mathematical Results in Quantum Physics, Hradec Kralove 6. September 2010

Title Discrete alloy type models: averaging and spectral properties Isaac Newton Institute for Mathematical Sciences, Cambridge, UK Invited talk at the workshop "Analysis on Graphs and its Applications Follow-up meeting" 29. July 2010

Title Spectral distribution function of percolation operators Department Mathematik, Universität Erlangen-Nürnberg AG Mathematische Physik 17. June 2010

### 2009

Title Discrete alloy type models with single site potentials of changing sign Clarion Congress Hotel Prague International Congress on Mathematical Physics, Invited talk in the section on Nonrelativistic Quantum Mechanics 4. August 2009

Title Geometrische und Spektrale Eigenschaften von Perkolationsclustern auf Cayleygraphen Universität Mainz job application talk 16. July 2009

Title Exponentieller Abfall der Greenschen Funktion für Legierungsmodelle auf $\Bbb Z$ Universität Oldenburg 10. July 2009

Title Percolation clusters on Calyey graphs and their spectra "Alp-Workshop", St.~Kathrein am Offenegg bei Graz 5. July 2009

Title Spektrale Eigenschaften von diskreten Legierungsmodellen Ruhr-Universität Bochum Oberseminar über Mathematische Physik 1. July 2009

Title Exponential decay of Green's function for Anderson models on $\Bbb Z$ with single-site potentials of finite support Universität Mainz Oberseminar Analysis 30. June 2009

Title Geometric and spectral properties of percolation on Cayley graphs Universität Paderborn job application talk 3. April 2009

Title Bounds on the spectral shift function and applications Durham University Pure Mathematics Colloquium 16. March 2009

Title Percolation clusters on Calyey graphs and their spectra Imperial College London Analysis and Probability Seminar 12. March 2009

Title Bounds on the spectral shift function and applications University College London Mathematics Seminar 11. March 2009

Title Geometric and spectral properties of percolation on Cayley graphs University of Bristol Analysis Seminar 9. March 2009

### 2008

Title Geometrische und spektrale Eigenschaften von Perkolationgraphen Institut für Mathematik, TU Berlin job application talk 17. December 2008

Title Perkolationscluster auf Cayleygraphen und deren Spektren Faculty of Mathematics, TU Cemnitz job application talk 12. December 2008

Title Percolation and spectra on Cayley-graphs Oberwolfach-Workshop "Interplay of Analysis and Probability in Physics" 2. December 2008

Title Geometrische und spektrale Eigenschaften von Perkolationgraphen TU Chemnitz Forschungsseminar Alogrithmische und Diskrete Mathematik 26. November 2008

Title Bounds on singular values of semigroup differences and the spectral shift function TU Clausthal Mathematisches Kolloquium 19. November 2008

Title Geometrische und spektrale Aspekte von Perkolation auf allgemeinen Graphen Fakultät für Mathematik und Informatik, Universität Bremen job application talk 18. November 2008

Title Perkolation auf homogenen Graphen Fakultät für Mathematik und Informatik, Fern-Universität Hagen job application talk 24. October 2008

Title Geometrische und spektrale Eigenschaften von Perkolationteilgraphen TU Dortmund Oberseminar Geometrie 23. October 2008

Title Perkolation auf homogenen Graphen School of Mathematics and Computer Science, Friedrich-Schiller-Universität of Jena job application talk 7. October 2008

Title Classical and Quantum percolation Institut für Mathematik C, Technische Universität Graz 28. July 2008

Title Singular values of semigroup differences and applications to the spectral shift function TU Berlin 24. July 2008

Title Geometrische und spektrale Eigenschaften von Perkolation auf Cayleygraphen Universität Tübingen job application talk 15. July 2008

Title Percolation on Cayley and quasi-transitive graphs Universität Bielefeld Workshop des SFB 701 "Aspects of Aperiodic Order" 4. July 2008

Title Geometrische und spektrale Eigenschaften von Perkolation auf Cayleygraphen Ruhr-Universität Bochum job application talk 1. July 2008

Title Estimates on singular values and the spectral shift function, with applications Universität Bielefeld job application talk 26. June 2008

Title Spectral and geometric properties of percolation on general graphs ESF-Conference "Operator Theory, Analysis and Mathematical Physics", Bedlewo, Polen 16. June 2008

Title Spectral and geometric properties of percolation on general graphs Institut für Mathematik, TU Clausthal Mathematisches Kolloquium 28. May 2008

Title Spectral and geometric properties of percolation on general graphs Institut for Theoretical Physics, Universität Hamburg Seminarreihe "Quantum Field Theory and Mathematical Physics" 27. May 2008

Title Integrated density of states for Schrödinger operators on metric graphs Humboldt Universiy of Berlin Workshop "Mathematical Physics and Spectral Theory" 25. April 2008

Title Wegner estimates for non-monotoneously correlated alloy type models Oberwolfach-Workshop, Disordered Systems: Random Schrödinger Operators and Random Matrices 25. March 2008

Title On spectral properties of correlated and non-monotone Anderson models German Open Conference on Probability and Statistics, Aachener Stochastiktage 6. March 2008

Title Spectral and geometric properties of percolation on general graphs Universität Bielefeld Seminar des SFB 701 23. January 2008

### 2007

Title Low energy asymptotics of percolation Laplacians on Cayley graphs Hausdorff-Institut, Bonn Workshop "Particle systems, nonlinear diffusions, and equilibration" 15. November 2007

Title Perkolationsprozesse und Laplaceoperatoren auf Cayleygraphen Philipps-Universität Marburg Kolloquium des Fachbereichs Mathematik und Informatik 15. August 2007

Title Low energy asymptotics of percolation Hamiltonians on graphs TU Wien Conference "Equadiff 07" 6. August 2007

Title Spectral asymptotics of percolation Laplacians on amenable Cayley graphs Isaac Newton Institute Workshop on "Quantum Graphs, Their Spectra and Applications" 3. April 2007

Title Lifshitz tails for random Hamiltonians monotone in the randomness Oberwolfach Mini-Workshop "Multiscale and variational methods in materials science and the quantum theory of solids" 12. February 2007

### 2006

Title Untere Schranken an Eigenwertabstände Chemnitzer Mathematisches Colloquium 7. December 2006

Title Lifshitz tails for the IDS of Schrödinger operators with random breather-type potential International Conference "Operator Theory in Quantum Physics", Prag 28. September 2006

Title Lifshitz tails for Schrödinger operators with random breather-type potential Conference "Operator Theory, Analysis and Mathematical Physics", Lund 16. June 2006

Title Existenz- und Stetigkeitseigenschaften der Integrierten Zustandsdichte Chemnitzer Mathematisches Colloquium 18. May 2006

Title Anderson-percolation Hamiltonians and compactly supported eigenstates Interdisciplinary Workshop "Evolution on Networks", Blaubeuren 1. May 2006

Title Untere Schranken an die unterste spektrale L¨cke von Hamiltonoperatoren mit singulärem Potential RWTH Aachen Seminar des Graduiertenkollegs "Hierarchie und Symmetrie in mathematischen Modellen" 24. April 2006

Title Anderson-percolation Hamiltonians and compactly supported eigenstates TU Graz Strukturtheorie-Seminar 20. April 2006

Title Spectral analysis of percolation Hamiltonians Oberwolfach Mini-Workshop on "$L^2$-Spectral Invariants and the Integrated Density of States" 24. February 2006

Title Tiefliegendes Spektrum von zufälligen Schrödingeroperatoren TU Chemnitz Forschungsseminar Algorithmische und Diskrete Mathematik 25. January 2006

Title Spectral properties of Anderson-percolation Hamiltonians on graphs Erwin Schrödinger Institut, Wien Workshop "Aspects of Spectral Theory" 19. January 2006

Title Compactly supported eigenfunctions of Hamiltonians on infinite graphs and jumps of the IDS Universität Bielefeld Seminar des SFB 701 4. January 2006

### 2005

Title Untere Schranken an die unterste spektrale Lücke von Hamiltonoperatoren mit singulärem Potential University Osijek, Croatia 19. December 2005

Title Lower bounds on the lowest spectral gap of singular potential Hamiltonians Universität Bonn Symposium "Dirichlet Forms, Stochastic Analysis and Interacting Systems" 24. November 2005

Title Lower bounds on the lowest spectral gap of singular potential Hamiltonians Université de Cergy-Pontoise, France 28. September 2005

Title Spectral Analysis of Percolation Hamiltonians Workshop "Computation and Analytic Problems in Spectral Theory", Gregynog, Wales 28. July 2005

Title Bounds on the spectral shift function and the density of states Max-Plank-Institut, Leipzig, Germany 24. May 2005

Title Localization for alloy-type models: rigorosus results and methods Department of Physics, Chemnitz 13. April 2005

Title Spectral analysis of percolation Hamiltonians Université Paris, France 8. March 2005

Title Quantenmechanik ungeordneter Festkörper: das Phänomen der Lokalisierung Kolloquium der Kroatischen Mathematischen Gesellschaft, Zagreb 23. February 2005

Title Spectral properties of periodic and random Schrödinger operators University of Bath, UK 14. February 2005

Title Spectral properties of the quantum percolation model on graphs University of Durham, UK 9. February 2005

### 2004

Title Bounds on the spectral shift function and the density of states TU Dresden November 2004

Title Spektren von Quantenperkolationsmodellen Universität Augsburg 22. November 2004

Title Spectral averaging induced by random, geometric perturbations Doppler Institute, Prag November 2004

Title Spectral Analysis of Percolation Hamiltonians QMath-9: Mathematical Results in Quantum Mechanics, Giens September 2004

Title Bounds on the spectral shift function and the density of states Mathematics and Physics of Disordered Systems, Oberwolfach May 2004

Title Spektrale Verschiebung induziert durch ein kompakt getragenes Potential Symposium über Analysis, Universitäat Basel April 2004

Title Integrated density of states for random metrics on manifolds City University of New York February 2004

### 2003

Title Spectral properties of the quantum percolation model on graphs Ruhr-Universität Bochum December 2003

Title Spectral shift induced by a compactly supported potential Universität Mainz December 2003

Title Spectral shift induced by a compactly supported potential Universität Stuttgart November 2003

Title Spectral shift induced by a compactly supported potential Universität Konstanz November 2003

Title Spectral shift induced by a compactly supported potential University of Alabama at Birmingham October 2003

Title Spectral shift induced by a compactly supported potential CalTech October 2003

Title Spectral shift induced by a compactly supported potential TU Chemnitz July 2003

Title Spectral shift induced by a compactly supported potential Ruhr-Universität Bochum July 2003

Title Spectral shift induced by a compactly supported potential University Zagreb July 2003

Title Spectral properties of quantum percolation models Conference Applied Mathematics and Scientific Computing, Brijuni, Kroatien 25. June 2003

Title Spectral properties of the quantum percolation model on graphs CalTech March 2003

Title Wegner estimates for indefinite potentials and inverses of Toeplitz matrices Western States Mathematical Physics Meeting, CalTech February 2003

### 2002

Title On Wegner estimates with singular and indefinite randomness UC Irvine 12. December 2002

Title Integrated density of states for random metrics on manifolds CalTech November 2002

Title Integrated density of states for random metrics on manifolds Ruhr-Universität Bochum October 2002

Title Existence of the density of states for single site potentials with samll support in one dimension Workshop Between Order and Disorder, Greifswald September 2002

Title Wegner estimate with local continuity requirements on the coupling constants Conference on Differential Equations and Mathematical Physics, Birmingham, USA 26. March 2002

Title Lokalisierung an Floquet-regulären Bandkanten Institut für Theoretische Physik I, Universität Erlangen-Nürnberg January 2002

Title Gruppoide von Neumann Algebren und die Integrierte Zustandsdichte Institut für Theoretische Physik I, Universität Erlangen-Nürnberg January 2002

Title Existenz der Zustandsdichte für indefinite Legierungspotentiale Fakultät für Mathematik, TU Chemnitz January 2002

### 2001

Title Lipschitz continuity of integrated density of states for single site potentials with small support Mathematical results in Quantum Mechanics, Taxco, Mexico December 2001

Title Integrated density of states for random operators on manifolds Workshop Schrödinger Operators, IIMAS, UNA Mexico 7. December 2001

Title Wegner estimate for sparse and other generalized alloy type potentials Workshop Schrödinger Operators, IIMAS, UNA Mexico 5. December 2001

Title The integrated Density of states and Wegner estimates Workshop Schrödinger Operators, IIMAS, UNA Mexico 3. December 2001

Title Existence of the density of states for Anderson models with indefinite single site potentials Workshop SFB 237, Tutzing October 2001

Title Integrated Density of states for random Schrödinger Operators on manifolds Mini-Conference Random Schrödinger Operators, Tsukuba, Japan August 2001

Title Wegner Estimate for Indefinite Anderson Potentials Research Institute for Mathematical Sciences, Kyoto Workshop Applications of Renormalization Group Methods in Mathematical Sciences July 2001

Title Wegner estimates for alloy type potentials with changing sign University of Osaka July 2001

Title Localization by disorder at Floquet-regular spectral boundaries University of Osaka July 2001

Title Regularity porperties of the integrated density of states of random Schrödinger operators Conference Applied Mathematics and Scientific Computing, Dubrovnik, Croatia June 2001

Title Die Wegner-Abschätzung und die gemeinsame Dichte der Anderson-Kopplungskonstanten Conference Schrödinger Operators, Oberwolfach June 2001

Title Spektrale Eigenschaften von periodischen und zufälligen Schrödingeroperatoren University Zagreb, Croatia May 2001

Title Wegner estimates for alloy type potentials with changing sign Schrödinger operators, Oberwolfach May 2001

Title Spektrale Eigenschaften von zufälligen Schrödingeroperatoren Fern-Universität Hagen March 2001

### 2000

Title Wegner Abschätzung für indefinite, überlappende Anderson Potentiale mit glatter Dichte AG Mathematische Physik, Bochum 5. October 2000

Title Wegner Abschätzung für indefinite, überlappende Einzelpotentiale mit glatter Dichte Workshop "Ungeordnete Systeme", Bochum May 2000

Title Integrated density of states for Schrödinger operators on manifolds Conference on Differential Geometry and Quantum Physics, Berlin May 2000

Title Integrated density of states for Schrödinger operators on manifolds Institut für Angewandte Mathematik, Universität Bonn January 2000

### 1999

Title Wegner Abschätzung für indefinite Anderson-Potentiale Workshop SFB 237, Bad Honnef September 1999

Title Wegner estimates for alloy type potentials with changing sign University of Lulea, Sweden September 1999

Title Wegner estimate for the Anderson model with indefinite potential NTNU Trondheim, Norway August 1999

Title Wegner estimate for the Anderson model with indefinite potential Conference on Differential Equations and Mathematical Physics, Birmingham, USA May 1999

### 1998

Title Random potentials causing localisation Workshop SFB 237, Bad Honnef September 1998

### Kontakt

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