# Prof. Dr. Ivan Veselić - Talks

### 2018

 Title: Uncertainty principles and null-controllability of the heat equation on bounded and unbounded domains Institution: University of Split Occasion: ApplMath18 Ninth Conference on Applied Mathematics and Scientific Computing, Solaris, Sibenik, Croatia Date: 17.-20. September 2018 Abstract: Null controllability for the heat equation In the talk I discuss several uncertainty relations for functions in spectral subspaces of Schroedinger 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-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.~Nakic, M. Taeufer, and M.~Tautenhahn, see \begin{itemize} \item Michela Egidi, Albrecht Seelmann, Ivica Nakic, Matthias Taeufer, Martin Tautenhahn, Ivan Veseli\'c: Null controllability and control cost estimates for the heat equation on unbounded and bounded domains, submitted (2018). \item Michela Egidi, Ivan Veselic: Scale-free unique continuation estimates and Logvinenko-Sereda Theorems on the torus, https://arxiv.org/abs/1609.07020, (2016). \item Michela Egidi, Ivan Veselic: Sharp geometric condition for null-controllability of the heat equation on $\mathbb{R}^d$ and consistent estimates on the control cost, https://arxiv.org/abs/1711.06088. \\ Arch. Math. 111:85-99, (2018). \item Ivica Nakic, Matthias Taeufer, Martin Tautenhahn, Ivan Veselic: Scale-free unique continuation principle, eigenvalue lifting and Wegner estimates for random Schroedinger operators, https://arxiv.org/abs/1609.01953, \\ Analysis \& PDE 11:1049-1081, (2018). \end{itemize}

 Title: Upper and lower Lipschitz bounds for the perturbation of edges of the essential spectrum Institution: Universitaet Bielefeld Occasion: Kolloquium Mathematische Physik" Date: 01. Juni 2018 Abstract: 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 is 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 talks is based on the preprint https://arxiv.org/abs/1804.07816

 Title: Uniform Approximation of the integrated density of states on amenable groups Institution: Bergische Universitaet Wuppertal Occasion: Workshop Ergodic Theory Date: 05. Mai 2018 Abstract:

 Title: Necessary and sufficient geometric condition for null-controllability of the heat equation on R^d. Institution: Fernuni Hagen Occasion: Workshop on "Control theory of infinite-dimensional systems" Date: 10. Januar - 12. Januar 2018 Abstract: In this talk we discuss the control problem for the heat equation on R^d, d≥1, with control set ω ⊂ R^d. We provide a sufficient and necessary condition (called (Γ,a)-thickness) on ω 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 R^d case. (This is joint work with Michela Egidid.)

### 2017

 Title: Glivenko Cantelli and Ergodic Theorem on groups. Institution: Ruhr Uni Bochum (RUB) Occasion: RTG 2131-Seminar Date: 23.10.2017

 Title: Glivenko Cantelli and Banach-space ergodic theorems applied to the uniform approximation of the integrated density of states Institution: Universität Trier Occasion: French-German meeting Aspect 17: Asymptotic Analysis and Spectral Theory Date: 25.September - 29.September 2017 Abstract: 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 Institution: Universität Potsdam Occasion: International Conference on Analysis and Geometry on Graphs and Manifolds Date: 31.Juli - 04.August 2017 Abstract: 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. Institution: Euler Institute, Saint-Petersburg, Russia Occasion: 9th Birman Conference in Spectral Theory Date: 03. Juli -06. Juli 2017 Abstract: Using Carleman estimates we prove scale free unique continuation estimates on boundedand 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 Institution: Bergische Universität Wuppertal Occasion: Hagen-Wuppertal Analysis-Treffen Date: 2. Mai 2017

 Title: Unique continuation estimates and the Logvinenko Sereda Theorem. Institution: Fernuni Hagen Occasion: Oberseminars Stochastik/Mathematische Physik Date: 15.02.2017 Abstract: 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 principle and its absence on continuum and discrete geometries

Institution:

Technische Universität Wien

Occasion:

Workshop on Operator Theory and Indefinite Inner Product Spaces

Date:

12. December 2016

Abstract:

A powerful tool in the analysis of solutions of partial di erential equations are unique continuation principles. Quantitative versions play an important role in inverse problems, uniqueness theorems for linear and non-linear di erential equations, and in the theory of random Schroedinger operators. On the contrary quantum graphs violate the continuation principle, giving rise to new phenom- ena. Certain graph Laplacians exhibit similar features.

Title:

#### Uncertainty relations and applications to the Schrödinger and heat conduction equations

Institution:

Johannes Gutenberg Universität Mainz

Occasion:

Summer school Mainz

Date:

13.September 2016

Abstract:

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

Institution:

University of Split School of Medicine, Split, Croatia

Occasion:

Summer school Split

Date:

27.August - 03.September 2016

Abstract:

Title:

#### Unique continuation principle and its absence on continuum space, on lattices and on quantum graphs

Institution:

WIAS Berlin

Occasion:

NewMET 2016

Date:

14.Juli - 15.Juli 2016

Abstract: 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

Institution:

Department of Mathematics, Faculty of Science, University of Zagreb, Croatia

Occasion:

International Workshop on PDEs: analysis and modelling Celebrating 80th anniversary of professor Nedžad Limić

Date:

19.Juni - 22.Juni 2016

Abstract: 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 & Veseli ́c, the generalization to linear combinations of
eigenfunctions to Naki ́c, Taeufer, Tautenhahn, & Veseli ́c.  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

Institution:
Occasion:

6th Croatian Mathematical Congress

Date: 16.Juni.2016
Abstract: 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

Institution: Fern-Universität Hagen
Occasion: Seminar Stochastik
Date: 4. Januar 2016

### 2015

Title:

#### Weihnachtsvorlesung "(Miss)Verständnis der Stochastik"

Institution: Technische Universität Chemnitz
Occasion:

#### Weihnachtsvorlesung am Tag der Lehre

Date: 3. Dezember 2015, 15:30 bis 17:00, Zentrales Hörsaalgebäude, Raum N112.
Abstract: 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) Institution: Zagreb University , Mathematics department Occasion: Colloquium of the Croatian Mathematical Society Date: 30. September 2015, 17:00 Abstract: 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. Link: 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) Institution: Zagreb University , Mathematics department Occasion: Probabilty seminar Date: 29. September 2015, 14:30 Link: http://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) Institution: Rijeka University, Department of Natural Sciences and Mathematics Occasion: Colloquium of the society of mathematicians and physicists Date: 28. September 2015, 12:00 Abstract: 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. Link: http://dmf.hr/2015/06/19/aproksimacija-i-ocjena-funkcija-na-osnovu-lokalnih-podataka/

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

 Title: Compressed sensing and the Calderon problem in electrical impedance tomography Institution: University of Split Occasion: Speech and Hearing Research Lab, School of Medicine Date: 17. September 2015, 11:00 Link: 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 Institution: Friedrich-Alexander-Universität Erlangen-Nürnberg Occasion: Tag der Stochastik Date: 10. July 2015, 14:00 Abstract: 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 Institution: Isaac Newton Institue, Cambridge Occasion: Workshop: Periodic and Other Ergodic Problems; 23 March - 27 March 2015 Date: 23. March 2015, 11:30 - 12:30 Co-authors: Ivica Nakic (Zagreb University), Matthias Täufer (TU Chemnitz), Martin Tautenhahn (TU Chemnitz) Abstract: 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 Institution: Isaac Newton Institue, Cambridge Occasion: Seminar Programme on Periodic and Ergodic Spectral Problems Date: 12. March 2015

 Title: Reconstruction and estimation of rigid functions based on local data Institution: Durham University Occasion: Geometry and Topology Seminar Date: 9. March 2015 Abstract: 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 Institution: Department of Mathematics, Bristol University Occasion: Mathematical Physics Seminar Date: 27. February 2015

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

### 2014

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

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

 Title: Quantitative unique continuation estimate and Wegner estimate for the standard random breather potential Institution: Pontificia Universidad Catolica de Chile Occasion: Einladung zum Plenarvortrag bei der International Conference Spectral Theory and Mathematical Physics Date: November 2014 Abstract: 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 Institution: Ecole des Ponts Paristech Date: 28. October 2014 Abstract: 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 Institution: Universität Paris 6 Occasion: Seminar Date: 27. Oktober 2014, 14:30

 Title: Uncertainty principles applied to observation and reconstruction of functions Institution: Universität Jena Occasion: Einladung zum Plenarvortrag beim meeting Mathematical Physics in Jena Date: 17. September 2014 Abstract: 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 Institution: TU Chemnitz Occasion: Chemnitz-Zagreb Workshop on Harmonic Analysis for PDE, Applications, and related topics Date: 1. July 2014, 10:00

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

 Title: Grenzverteilungssäatze für stochastische Modelle komplexer physikalischer Systeme Institution: Universität Jena Occasion: Stochastisches Kolloquium Date: June 2014

 Title: Grenzverteilungssätze für Modelle ungeordneter Systeme Institution: Universität zu Köln Occasion: Workshop Stochastik Date: January 2014

 Title: Eigenwert-Statistiken und -Verteilungsfunktionen Institution: Fern-Universität Hagen Occasion: Oberseminar Stochastik Date: January 2014

 Title: Eigenwert-Statistiken und -Verteilungsfunktionen Institution: Universität Wuppertal Occasion: Oberseminar Stochastik Date: 22. January 2014, 15:00 Abstract: 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 Institution: Universität Bonn Occasion: Seminar Stochastic and Geometric Analysis Date: January 2014, 10:00

### 2013

 Title: Multiscale unique continuation properties of eigenfunctions Institution: Universität Zagreb Occasion: Numerical Analysis Seminar Date: October 2013

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

 Title: Integralabschätzungen für Eigenfunktionen auf multiplen Skalen Institution: TU Chemnitz Occasion: Forschungsseminar Harmonische Analysis Date: July 2013

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

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

### 2012

 Title: Equidistribution properties of PDE-eigenfunctions Institution: Institute of Mathematics of Bordeaux, University Bordeaux 1 Occasion: Conference Spectral Theory and Its Applications Date: 4. October 2012, 09:00 Abstract: 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 Institution: Johannes Gutenberg-Universität Mainz Occasion: Trilateral German-French-Russian Workshop on Asymptotic analysis and spectral theory on non-compact structures Date: September 2012

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

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

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

 Title: Glivenko-Cantelli-Theorems, concentration inequalities, and the IDS Institution: Institut de Mathématiques de Jussieu, Université Paris 13 Occasion: Conference: Mathématiques des systémes quantiques désordonnés Date: 29. May 2012, 10:50 Abstract: 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 Institution: Universität Jena, Lehrstuhl für Analysis Occasion: Oberseminar Analysis, Geometrie und Stochastik Date: 11. May 2012, 11:15

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

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

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

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

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

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

 Title: Skaleninvariantes quantitatives Eindeutiges-Fortsetzungsprinzip und Anwendungen Institution: Seminar Analysis, TU Dresden Abstract: PDF-file Occasion: Analysis Seminar Date: 19. January 2012

### 2011

 Title: Scale-free quantitative unique continuation principle Institution: Max-Planck-Institut füur Mathematik in den Naturwissenschaften, Leipzig Abstract: PDF-file Occasion: Analysis Seminar Date: 15. December 2011

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

 Title: Unique continuation principle and Wegner estimates Institution: Mathematisches Forschungsinstitut Oberwolfach Abstract: PDF-file Occasion: Workshop "Correlations and Interactions for Random Quantum Systems" Date: 24. October 2011

 Title: Unique continuation properties of solutions of elliptic second order differential equations (1) and (2) Institution: TU Chemnitz Occasion: Seminar "Partielle Differentialgleichungen und Inverse Probleme" Date: 21. October 2011 and 11.November 2011 Abstract: 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 Institution: Mathematical Society in Split Occasion: Colloquium Date: 21. September 2011

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

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

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

 Title: Zufällige Schrödingeroperatoren mit nicht-monotoner Parameter-Abhängigkeit Institution: Johannes Gutenberg-Universität Mainz Date: 28. Januar 2011

### 2010

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

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

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

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

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

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

### 2009

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

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

 Title: Exponentieller Abfall der Greenschen Funktion fü Legierungsmodelle auf Z Institution: Universität Oldenburg Date: 10. July 2009

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

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

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

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

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

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

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

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

### 2008

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

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

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

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

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

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

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

 Title: Geometrische und spektrale Eigenschaften von Perkolationteilgraphen Institution: TU Dortmund Occasion: Oberseminar Geometrie Date: 23. October 2008

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

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

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

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

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

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

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

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

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

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

 Title: Integrated density of states for Schr\"odinger operators on metric graphs Institution: Humboldt-Universiy Berlin Occasion: Workshop "Mathematical Physics and Spectral Theory" Date: 25. April 2008

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

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

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

### 2007

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

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

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

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

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

### 2006

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

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

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

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

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

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

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

 Title: Spectral analysis of percolation Hamiltonians Occasion: Oberwolfach Mini-Workshop "L2-Spectral Invariants and the Integrated Density of States" Date: 24. February 2006

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

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

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

### 2005

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

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

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

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

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

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

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

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

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

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

### 2004

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

 Title: Spektren von Quantenperkolationsmodellen Istitution: Universität Augsburg Date: 22. November 2004

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

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

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

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

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

### 2003

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

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

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

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

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

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

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

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

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

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

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

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

### 2002

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

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

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

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

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

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

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

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

### 2001

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

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

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

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

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

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

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

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

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

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

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

 Title: Spektrale Eigenschaften von periodischen un zufälligen Schrödingeroperatoren Institution: University Zagreb, Croatia Date: May 2001

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

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

### 2000

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

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

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

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

### 1999

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

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

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

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

### 1998

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

### Kontakt

TU Dortmund
Fakultät für Mathematik
Lehrstuhl IX
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44227 Dortmund

Sie finden uns auf dem sechsten Stock des Mathetowers .

Sekretariat: Janine Textor
Raum M 620

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janine.textor@tu-dortmund.de

Tel. (0231) 755-3063
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