Research

• Geometry and spectral theory of Dirichlet spaces
  
  
• Random and equivariant Schrödinger operators
  
  
• Aperiodic order and dynamical systems of low complexity

Research supported by German Research Foundation (DFG) in Einzelförderung ' Green's formulae and harmonic functions for graphs and Dirichlet spaces - follow up' (Joint with Prof. Dr. Matthias Keller and Dr. Marcel Schmidt), 2018 - 2024.

Research supported by German Research Foundation (DFG) within Schwerpunktprogramm 'Geometry at infinity', 2017- 2025.

Research supported by German Research Foundation (DFG) within Graduiertenkolleg 'Quanten- und Gravitationsfelder'  2013 - 2017.

Research supported  by German Research Founddation (DFG) in Einzelförderung 'Geometry of discrete spaces and spectral theory of non-local operators' (joint with Dr. Matthias Keller),   2012-2018. 

Research supported by German Research Foundation (DFG) in Einzelföderung 'Zuf\"allige und periodische Quantengraphen', 2009 - 2014.

Research supported by German Research Foundation (DFG) in Einzelförderung  'Delone dynamische Systeme: Ergodentheorie, Diffraktion und Operatortheorie'    (joint project with Prof. Dr. P. Stollmann), 2004 - 2008.

Research supported by  German Research Foundation (DFG) within Schwerpunktprogramm "Quasikristalle"  (joint project with Prof. Dr. P. Stollmann), 2001 - 2003.

The following list does not include the publication information for all articles. See MathSciNetExterner Link or zbMathExterner Link for details.

• Graphs at infinity: Liouville theorems, Recurrence and Characterization of Dirichlet forms (with Matthias Keller, Marcel Schmidt), arXiv:2604.14979 
  
  
• Wiener--Wintner points for topological dynamical systems (with Nicolae Strungaru), arXiv:2510.18056 
  
  
• Which Meyer sets are regular model sets? A characterization via almost periodicity (with Christoph Richard, Nicolae Strungaru), arXiv:2410.22536 
  
  
• Diffraction as a unitary representation and the orthogonality of measures with respect to the reflected Eberlein convolution (with Nicolae Strungaru),  (2402.01044Externer Link)
  
  
• Pure point diffraction and almost periodicity (with Timo Spindeler, Nicolae Strungaru), arXiv:2312.12825 
• Note on intrinsic metrics on graphs (with Marcel Schmidt, Felix Seifert), (2308.12664Externer Link)
• Recurrent and (strongly) resolvable graphs (with Simon Puchert, Marcel Schmidt), (2301.01994Externer Link)
  
  
• Boundary representations of intermediate forms between a regular Dirichlet form and its active main 
  part (with Matthias Keller, Michael Schwarz, Marcel Schmidt, Melchior Wirth), (2301.01035Externer Link)
  
  
• Boundary representations of intermediate forms between a regular Dirichlet form and its active main 
  part (with Matthias Keller, Michael Schwarz, Marcel Schmidt, Melchior Wirth), (2301.01035Externer Link)
  
  
• The (twisted) Eberlein convolution of measures (with Timo Spindeler, Nicolae Strungaru),      (2211.06969Externer Link)
  
  
• Abstract almost periodicity for group actions on uniform topological spaces (with Timo Spindeler, Nicolae Strungaru), (2208.01304Externer Link)
  
  
• Uniformity Aspects of SL(2,R) Cocycles and Applications to Schrödinger Operators Defined Over Boshernitzan Subshifts (with David Damanik), (2207.12153Externer Link)
  
  
• Blow-up of nonnegative solution of an abstract  semilinear heat equation with convex source (with Marcel Schmidt, Ian Zimmermann), (2108.11291Externer Link)  

• On L^p Liouville theorems for Dirichlet forms (with Bobo Hua, Matthias Keller, Marcel Schmidt), (2108.11678Externer Link) 
  
  
• Pure point spectrum for dynamical systems and mean almost periodicity (with Timo Spindeler, Nicolae Strungaru),  (2006.10825Externer Link)
  
  
• Pure Point Diffraction and Mean, Besicovitch and Weyl Almost Periodicity  (with Timo Spindeler, Nicolae Strungaru), (2006.10821Externer Link)
  
  
• Self-Adjoint Extensions of Bipartite Hamiltonians (with Timon Weinmann, Melchior Wirth), to appear in: Proc. Edinburgh Math. Soc. (1912.03670Externer Link)
  
  
• Absence of Absolutely Continuous Spectrum for Generic Quasi-Periodic Schrödinger Operators on the Real Line  (with David Damanik), to appear in: Israel J. Math. (1909.00378Externer Link)
  
  
• Modulated crystals and almost periodic measures (with Jeong-Yup Lee, Christoph Richard, Bernd Sing, Nicolae Strungaru) to appear in: Lett. Math. Phys. (1907.07017Externer Link)
  
  
• Subshifts with leading sequences, uniformity of cocycles and spectral theory of Schreier graphs (with Rostislav Grigorchuk, Tatiana Nagnibeda, Daniel Sell). (1906.01898Externer Link)
  
  
• Universal lower bounds for Laplacians on weighted graphs (with Peter Stollmann), to appear in: Analysis and Geometry on Graphs and Manifolds, eds: Matthias Keller, Daniel Lenz, Radoslaw Wojciechowski, London Mathematical Society Lecture Note Series 461.  (1903.02382Externer Link)
  
  
• The structure of mean equicontinuous group Actions (with Gabriel Fuhrmann, Maik Gröger), to appear in: Israel J. Math. (1812.10219Externer Link)
  
  
• Spectral theory of dynamical systems as diffraction theory of sampling functions, to appear in:  Monatshefte f. Mathematik  (1809.07639Externer Link)
  
  
• Topological Poincare type  inequalities and lower bounds on the infimum of the spectrum for graphs (with Marcel Schmidt, Peter Stollmann). (1801.09279Externer Link)
  
  
• Geometric properties of Dirichlet forms under order isomorphism (with Marcel Schmidt, Melchior Wirth). (1801.08326Externer Link)
  
  
• Combinatorics of the subshift associated to Grigorchuk's group (with Rostislav Grigorchuk, Tatiana Nagnibeda),  (Russian) Tr. Mat. Inst. Steklova   297   (2017), Poryadok i Khaos v Dinamicheskikh Sistemakh, 158--164.  (1711.10342Externer Link)
  
  
• Boundary representation of Dirichlet forms on discrete spaces (with Matthias Keller, Marcel Schmidt, Michael Schwarz), J. Math. Pures App. 126 (2019), 109--143.  (1711.08304Externer Link)
  
  
• Domination of quadratic forms (with Marcel Schmidt, Melchior Wirth), to appear in: Mathematische Zeitschrift  (1711.07225Externer Link)
  
  
• On the decomposition principle and a Persson type theorem for general regular Dirichlet forms (with Peter Stollmann),   J.  Spectr.  Theory  9   (2019),   1089--1113.. (1705.10398Externer Link)
  
  
• Averaging almost periodic functions along exponential sequences (with Michael Baake, Alan Haynes),  in: Aperiodic order: Volume 2, Crystallography and Almost Periodicity.  (Eds M. Baake, U. Grimm), Cambridge University Press, (2017).   (1704.08120Externer Link)
  
  
• Diffusion on Delone sets (with Sebastian Haeseler, Xuping Huang, Felix Pogorzelski),  J. Stat. Phys. 167  (2017),  1496--1510.  (1611.01059).Externer Link
  
  
• On weakly almost periodic measures (with Nicolae Strungaru),  Trans. Amer. Math. Soc.  371 (2019), 6843--6881.  (1609.08219Externer Link)
  
  
• Uniqueness of form extensions and domination of semigroups (with Melchior Wirth, Marcel Schmidt), to appear in: J. Funct. Anal.  (1608.06798Externer Link)
  
  
• An autocorrelation and discrete spectrum for dynamical systems on metric spaces, to appear in: Ergodic Theory & Dynamical Systems  (1608.05636Externer Link)
  
  
• On the spectrum of operator families on discrete groups over minimal dynamical systems (with Siegfried Beckus, Marko Lindnder, Christian Seifert),   Math. Z.  287     (2017),    993--1007.  (1606.08353Externer Link)
  
  
• An uncertainty principle and lower bounds for the Dirichlet Laplacian on graphs (with Peter Stollmann, Guenter Stolz), to appear in: J. Spectral Theory.   (1606.07476Externer Link)
  
  
• Model sets with positive entropy in Euclidean cut and project schemes (with Tobias Jaeger, Christian Oertel), to appear in: Ann.  sc. ENS.  (1605.01167Externer Link)
  
  
• Spectral notions of aperiodic order (with Michael Baake),  Discrete Contin. Dyn. Syst. Ser. S  10  (2017),  161--190. (1601.06629Externer Link)
  
  
• Toeplitz flows and model sets (with Michael Baake, Tobias Jaeger), Bull. London Math. Soc. 48 (2016), 691--698. (1511.08595Externer Link)
  
  
• Schreier graphs of Grigorchuk's group and a subshift associated to a non-primitive Substitution (with Rostislav Grigorchuk,  Tatiana Nagnibeda), to appear in: Groups, Graphs and Random Walks, T. Ceccherini-Silberstein, M. Salvatori, E. Sava-Huss, (Eds), London Math. Soc. Lecture Note Series, Cambridge  University Press  (2017).  (1510.00545Externer Link)
  
  
• Note on short time behavior of semigroups associated to selfadjoint Operators (with Matthias Keller, Florentin Münch, Marcel Schmidt, Andras Telcs),  Bull. London Math. Soc. 48 (2016), 935--944.  (1509.01993Externer Link)
  
  
• Invariant means on Boolean inverse monoids (with Ganna Kudryavtseva, Mark Lawson, Pedro Resende),  Semigroup Forum 92 (2016), 77--101.  (1503.03733)Externer Link
  
  
• Note on the set of Bragg peaks with high intensity (with Nicolae Strungaru),  Ann. Henri Poincare 17 (2016), 673--687. (1412.7377)
  Externer Link
• Spectra of Schreier graphs of Grigorchuk's group and Schroedinger operators with aperiodic order (with Rostislav Grigorchuk, Tatiana Nagnibeda),   Math. Ann.   370 (2018), 1607 --1637.    (1412.6822)Externer Link
  
  
• Note on spectra of non-selfadjoint operators over dynamcial systems (with Siegfried Beckus, Marko Lindnder, Christian Seifert),  Proc. Edinburgh Math. Soc.  61 (2018), 371--386.   (1412.5926)
  
  
• Global properties of Dirichlet forms in terms of Green's formula (with Sebastian Haeseler, Matthias Keller, Jun Masamune, Marcel Schmidt),   Calc. Var. PDE 56  (2017),   43 pp.  (1412.3355Externer Link)
  
  
• Note on uniformly transient graphs (with Matthias Keller, Marcel Schmidt, Radek Wojciechowski), Rev. Mat. Iberoam.  33  (2017),   831--860.  (1412.0815Externer Link)
  
  
• The Ihara Zeta function for infinite graphs (with Felix Pogorzelski, Marcel Schmidt),  Trans. Amer. Math. Soc. 371 (2019), 5687--5729.   (1408.3522Externer Link)
  
  
• Equicontinuous factors, Proximality and Ellis semigroup for Delone sets (with Jean-Baptiste Aujogue, Marcy Barge, Johannes Kellendonk), in:  Mathematics of Aperiodic Order (eds. J. Kellendonk, D. Lenz, J. Savinien), Progress in Mathematics 309, Birkhaeuser,  (1407.1787Externer Link)
  
  
• Diffusion determines the recurrent graph (with Matthias Keller, Marcel Schmidt, Melchior Wirth),  Advances in Mathematics 269 (2015), 364--398.  (1405.3256)Externer Link
  
  
• An invitation to trees of finite cone type: random and deterministic Operators (with Matthias Keller, Simone Warzel), Markov Processes Relat. Fields 21 (2015), 557--574.     (1403.4426)Externer Link
  
  
• Expansion in generalized eigenfunctions for Laplacians on graphs and metric measure spaces (with Alexander Teplyaev), Trans. Amer. Math. Soc.   368 (2016),  4933--4956.  (1310.5650)Externer Link
  
  
• Graphs of finite measure (with Agelos Georgakopoulos, Sebastian Haeseler, Matthias Keller, Radek Wojciechowski),   J. Math. Pures Appl.   103 (2015), 1093--1131.  (1309.3501)Externer Link
• Zero measure Cantor spectra for continuum one-dimensional quasicrystals (with Christian Seifert, Peter Stollmann), J. Diff. Eqn. 256 (2014), 1905--1926. (1308.3431)
  Externer Link
• Dynamical versus diffraction spectrum for structures with finite local complexity (with Michael Baake, Aernout van Enter),  Ergodic Theory & Dynamical Systems   35  (2015),  2017--241.  (1307.7518Externer Link)
• New relations between discrete and continuous transition operators on (metric) graphs (with Konstantin Pankrashkin),  Integral Equations and Operator Theory 84 (2016), 151--181.   (1305.7491Externer Link)
   
• Distributive inverse semigroups and non-commutative Stone dualities (with Mark Lawson), (1302.3032)
  Externer Link 
• Unbounded quantum graphs with unbounded boundary conditions (with Carsten Schubert and Ivan Veselic),  Math. Nachr.  287 (2014), 962--979.  (1205.1944)Externer Link
  
  
• Delone sets  with finite local complexity: Linear repetitivity versus positivity of weights (with Adnene Besbes, Michael Boshernitzan), Discrete and Computational Geometry   49 (2013), 335--347. (1202.6023)
  Externer Link
• Stationary processes with pure point diffraction (with Robert V. Moody),  Ergodic Theory & Dynamical Systems  37  (2017),  2597--2642.    (1111.3617)Externer Link
  
  
• A characterization of subshifts with bounded powers (with Johannes Kellendonk and Jean Savinien),  Disc. Math. 313 (2013), 2881--2894.  (1111.1609Externer Link)
  
  
• Absolutely continuous spectrum for random operators on trees of finite cone type (with Matthias Keller and Simone Warzel),  Journal d' Analyse Mathematique  118 (2012), 363---396.   (1108.0057)Externer Link
  
  
• Pseudogroups and their etale groupoids (with Mark V. Lawson), Advances in Mathematics 244 (2013), 117--170.  (1107.5511Externer Link)
   
• Equicontinuous Delone dynamical systems (with Johannes Kellendonk), Canadian Journal of Mathematics 65 (2013), 149--170.    (1105.3855).Externer Link
  
  
• Volume Growth, Spectrum and Stochastic Completeness of Infinite Graphs (with Matthias Keller, Rados{\l}aw Wojciechoswki), Mathematische Zeitschrift  274 (2013), 905--932.   (1105.0395)Externer Link.
  
  
• Laplacians on infinite graphs: Dirichlet and Neumann  boundary conditions (with Sebastian Haeseler, Matthias Keller, Rados{\l}aw Wojciechowski),   Journal of Spectral Theory  2 (2012), 397--432.   (1103.3695).Externer Link
  
  
• Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation (with Matthias Keller), Math. Model. Nat. Phenom. 5 (2010), 198--224.  (1101.2979)Externer Link
  
  
• Note on basic features of large time behaviour of heat kernels (with Matthias Keller, Hendrik, Vogt,  Rados{\l}aw Wojciechowski),  J. reine  angew. Math. (Crelles Journal) 708 (2015),  73--95.   (1101.0373)Externer Link
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• Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory (with Rupert Frank, Daniel Wingert), J. Funct. Anal. 266 (2014),  4765--4808.  (1012.5050)Externer Link
  
  
• L^p approximation of the integrated density of states for Schrödinger operators with finite local complexity (with Michael Gruber, Ivan Veselic), Integr. Equ. Oper. Theory  69, (2011), 217--232.  (1004.3471)Externer Link
  
  
• A Banach space valued ergodic theorem and uniform approximation of the integrated density of states (with Fabian Schwarzenberger, Ivan Veselic),  Geometriae Dedicata 150 (2011), 1--34.   (1003.3620)Externer Link, Erratum: Geometriae Dedicata 159 (2012), 411--413.
  
  
• Delone measures of finite local complexity and applications to spectral theory of one-dimensional continuum models of quasicrystals  (with Steffen Klassert, Peter Stollmann),  Discrete and Continuous Dynamical Systems - Series  A  29 (2011),  1553--1571. (1003.3574)Externer Link
  
  
• On the spectral theory of trees with finite cone type (with Matthias Keller, Simone Warzel),  Israel Journal of Mathematics  194 (2013),  107--135. (1001.3600)Externer Link
  
  
• Note on powers in three interval exchange transformations (with Zuzana Masakova, Edita Pelantova),   Theoret. Comput. Sci. 412 (2011), 3788--3794.    (0909.1109)Externer Link
  
  
• Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms (with  Peter Stollmann, Ivan Veselic),  Oper. Theory Adv. Appl. 214 (2011),  83--106.  (0909.1107)Externer Link
  
  
• An uncertainty principle, Wegner estimates and localization near fluctuation boundaries (with Anne Boutet de Monvel, Peter Stollmann),  Math. Z. 269 (2011), 663--670.   (0905.2845)Externer Link
  
  
• Dirichlet forms and stochastic completeness of graphs and subgraphs (with Matthias Keller), J. reine angew. Math. (Crelles Journal) 666 (2012), 189--223.   (0904.2985)Externer Link
  
  
• Compactness of Schrodinger semigroups (with Peter Stollmann, Daniel Wingert),  Math. Nachrichten 283 (2010), 94--103. (0903.0280)Externer Link
  
  
• Mini-Workshop: The Pisot Conjecture - from Substitution Dynamical Systems to Rauzy Fractals and Meyer Sets. Abstracts from the mini-workshop held March 1-7, 2009. Organized by Valerie Berthe, David Damanik and Daniel Lenz. Oberwolfach Reports. Vol 6. no 1.  (2009),  725--766.Externer Link
  
  
• Continuity of the integrated density of states on random length metric graphs (with Norbert Peyerimhoff, Olaf Post, Ivan Veselic'),  Mathematical Physics, Analysis and Geometry  12 (2009), 219--254.  (0811.4513)Externer Link
  
  
• The Allegretto-Piepenbrink Theorem for strongly local forms (with Peter Stollmann, Ivan Veselic),  Documenta Mathematica  14 (2009), 167--189.   (0811.2135)Externer Link
  
  
• Extinctions and correlations for uniformly discrete point processes with pure point spectrum (with Robert V. Moody),   Commun. Math. Phys. 289, (2009), 907--923.  (0902.0567)Externer Link
  
  
• Aperiodic order and pure point diffraction, The Philosophical Magazine, 88 (2008), 2059-2071 (Special Issue: Quasicrystals: the silver jubilee) (0802.324)Externer Link
  
  
• Eigenfunction expansion for Schrodinger operators on metric graphs (with Carsten Schubert, Peter Stollmann), Integral Equations and Operator Theory 62 (2008), 541--553. (0801.1376)Externer Link
  
  
• Uniform existence of the integrated density of states for combinatorial and metric graphs over Z^d (with Michael Gruber, Ivan Veselic), in: Analysis on Graphs and its Applications (edited by P. Exner, J. Keating, P.Kuchment T. Sunada and A. Teplyaev), Proceedings of Symposia in Pure Mathematics 77 (0712.1740)Externer Link
  
  
• Aperiodic order via dynamical systems: Diffraction theory for sets of finite local complexity, Contemp. Math. 485 (Ergodic Theory, Idris Assani, ed), (2009), 91 --112. (0712.1323)Externer Link
  
  
• Hamiltonians on discrete structures: Jumps of the integrated density of states and uniform convergence (with Ivan Veselic),   Mathematische Zeitschrift 263 (2009), 813--835.   (0709.2836)Externer Link
  
  
• Sch'nol's Theorem For Strongly Local Forms (with Anne Boutet de Monvel, Peter Stollmann), Israel Journal of Mathematics 173 (2009), 189--211. (0708.1501)Externer Link
  
  
• Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies (with Michael Baake, Christoph Richard), Lett. Math. Phys. Volume 82, (2007), 61--77. (0706.1677)Externer Link
  
  
• Continuity properties of the integrated density of states on manifolds (with Norbert Peyerimhoff, Olaf Post, Ivan Veselic), Japanese Journal of Mathematics, 3 (2008), 121--161. (0705.1079)Externer Link
  
  
• Pure point spectrum for measure dyamical systems on locally compact Abelian groups (with Nicolae Strungaru),  J. Math. Pures Appl. 92 (2009), 323--341.  (0704.2498)Externer Link
  
  
• Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over $\mathbb{Z}^d$ (with Michael J. Gruber, Ivan Veselic), J. Funct. Anal. Volume 253, (2007), 515--533. (math.0612743)Externer Link
  
  
• Continuity of eigenfunctions of uniquely ergodic dynamical systems and intensity of Bragg peaks, Commun. Math. Phys. 287 (2009), 225--258. (math-ph/0608026)Externer Link
  
  
• Uniform existence of the integrated density of states for models on $\ZZ^d$ (with Peter Mueller and Ivan Veselic), Positivity 12 (2008), 571 - 589. (math-ph/0607063)Externer Link
  
  
• Mini-workshop: $L\sp 2$-Spectral Invariants and the Integrated Density of States. Abstracts from the mini-workshop held February 19--25, 2006. Organized by Jozef Dodziuk, Daniel Lenz, Thomas Schick and Ivan Veseli\'c. Oberwolfach Reports. Vol. 3, no. 1. (2006), no. 1, 511--552.Externer Link
  
  
• Pure point diffraction and cut and project schemes for measures: The smooth case (with Christoph Richard), Mathematische Zeitschrift 256, (2007), 347--378. (math.DS/0603453)Externer Link
  
  
• On an order based construction of a groupoid from an inverse semigroup, Proc. Edinburgh Math. Soc. 51 (2008), 387--406. (math.OA/0604105)Externer Link
  
  
• Uniform Szego Cocycles Over Strictly Ergodic Subshifts (with David Damanik), Journal of approximation theory 144, (2007), 133-138. (math.SP/0512033)Externer Link
  
  
• Characterizations of model sets by dynamical systems (with Michael Baake, Robert V. Moody), Ergodic Theory & Dynamical Systems 27, (2007), 341-382. (math.DS/0511648)Externer Link
  
  
• Mini-Workshop: Dynamics of Cocycles and One-Dimensional Spectral Theory. Abstracts from the mini-workshop held November 13--19, 2005. Organized by David Damanik, Russell Johnson and Daniel Lenz. Oberwolfach Reports. Vol. 2, no. 4. (2005), 2933--2978.Externer Link
  
  
• Generic subsets in spaces of measures and singular continuous spectrum (with Peter Stollmann), in: Lecture Notes in Physics 690, Springer (2006)
  
  
• Lower Transport Bounds for One-Dimensional Continuum Schr\"odinger Operators (with David Damanik, Guenter Stolz ), Math. Ann. 336, (2006), 361--389 (math-ph/0410062 )Externer Link
  
  
• Elliptic operators on planar graphs: Unique continuation for eigenfunctions and nonpositive curvature (with Steffen Klassert, Norbert Peyerimhoff, Peter Stollmann), Proceedings of the American Mathematical Society, 134, (2006) 1549--1559. (math-ph/0410022)Externer Link
  
  
• Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians (with Peter Stollmann), Duke Math. J. 131, (2006), 203--217. (math-ph/0410021)Externer Link
  
  
• Zero-measure Cantor spectrum for Schrodinger operators with low-complexity potentials (with David Damanik) J. Math. Pures Appl. (9) 85 (2006), 671--686
  
  
• Deformation of Delone dynamical systems and pure point spectrum (with Michael Baake), Journal of Fourier Analysis and Applications, 11, (2005), 125 --150 (math.DS/0404155)Externer Link
  
  
• A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem (with David Damanik), Duke Math. J. 133 (2006), 95--123
  
  
• An ergodic theorem for Delone dynamical systems and existence of the integrated density of states (with Peter Stollmann), J. d' Analyse Mathematique 97, (2006), 1 --23. (math-ph/0310017)Externer Link
  
  
• Singular continuous spectrum for certain quasicrystal Schrödinger operators, Contemporary Mathematics 364, 169--180
  
  
• Substitution dynamical systems: Characterization of linear repetitivity and applications (with David Damanik), J. Math. Anal. Appl. 321 (2006), 766--780 (math.DS/0302231)Externer Link
  
  
• Aperiodic order and quasicrystals: spectral properties, Annales Henri Poincare 4, suppl 2 (2004). (with Peter Stollmann)
  
  
• Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra (with Michael Baake), Ergodic Theory & Dynamical Systems 24 (2004), 1867-1893. (math.DS/0302061)Externer Link
  
  
• Ergodic theory and discrete one-dimensional random Schr"odinger operators: uniform existence of the Lyapunov exponent, Contemporary Mathematics 327 (2003), 223--238.
  
  
• Integrated density of states for random metrics on manifolds (with Norbert Peyerimhoff and Ivan Veselic), Proc. London Math. Soc. 88 (2004), 733--752. (math-ph/0212058)Externer Link
  
  
• Random Schr"odinger operators on manifolds (with Norbert Peyerimhoff and Ivan Veselic), Markov Process. Related Fields 9 (2003), 717--728, proceedings of the conference "Aspects Mathematiques des Systemes Aleatoires et de la Mecanique Statistique", held in the honour of L. Pastur, May 2002, Marseille (math-ph/0212057)Externer Link
  
  
• Delone dynamical systems: ergodic features and applications (with Steffen Klassert and Peter Stollmann), in: Quasicrystals, Structure and Physical Properties, H.-R. Trebin (ed.), Wiley-VCH, Berlin (2003), 172--187.
  
  
• Algebras of random operators associated to Delone dynamical systems (with Peter Stollmann), Mathematical Physics, Analysis and Geometry 6 (2003), 269--290. (math-ph/0210031)Externer Link
  
  
• Aperiodic linearly repetitive Delone sets are densely repetitive, Discrete Comput. Geom. 31 (2004), 323--326. (math.MG/0208132)Externer Link
  
  
• Discontinuities of the integrated density of states for random operators on Delone sets (with Steffen Klassert and Peter Stollmann), Commun. Math. Phys. 241 (2003), 235--243. (math-ph/0208027)Externer Link
  
  
• Existence of non-uniform cocycles on uniquely ergodic systems, Ann. Inst. Henri Poincare: Prob. & Stat. 40 (2004), 197--206.
  
  
• Powers in Sturmian sequences (with David Damanik), European J. Combin. 24 (2003), 377--390.
  
  
• Groupoids, von Neumann Algebras and the Integrated Density of States (with Norbert Peyerimhoff and Ivan Veselic), Math. Phys. Anal. Geom. 10 (2007), 1--41. (arXiv:math-ph/0203026)Externer Link
  
  
• Delone dynamical systems and associated random operators (with Peter Stollmann), Conference Proceedings, Constanta (Romania), July 2-7, 2001, J.-M. Combes, J. Cuntz, G.A. Elliott, G. Nenciu, H. Siedentop, S. Stratila (eds.), Theta Foundation, ISBN 973-85432-2-3. (arXiv:math-ph/0202042)Externer Link
  
  
• Quasicrystals, aperiodic order, and groupoid von Neumann algebras (with Peter Stollmann), C. R. Acad. Sci. Ser. I, 334 (2002), 1131--1136.
  
  
• Uniform spectral properties of one-dimensional quasicrystals, IV. quasi-Sturmian potentials (with David Damanik), J. d' Analyse Mathematique 90 (2003), 115--139. (arXiv:math-ph/0105034)Externer Link
  
  
• Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals, Commun. Math. Phys., 227 (2002), 119--130. (arXiv:math-ph/0106012)Externer Link
  
  
• Uniform ergodic theorems on subshifts over a finite alphabet, Ergodic Theory & Dynamical Systems, 22 (2002), 245--255. (arXiv:math.DS/0005067)Externer Link
  
  
• The index of Sturmian sequences (with David Damanik), European Journal of Combinatorics, 23 (2002), 23--29.
  
  
• Linear repetitivity I., Uniform subadditive ergodic theorems and applications (with David Damanik), Discrete and Computational Geometry, 26 (2001), 411-428. (arXiv:math.DS/0005062)Externer Link
  
  
• Half-line eigenfunction estimates and singular continuous spectrum of zero Lebesgue mesasure (with David Damanik), Forum Mathematicum 16 (2004), 109--128 (arXiv:math.SP/9905099)Externer Link
  
  
• Uniform spectral properties of one-dimensional quasicrystals, III. $\alpha$-continuity (with David Damanik and Rowan Killip), Commun. Math. Phys. 212 (2000), 191-204. (arXiv:math-ph/9910017)Externer Link
  
  
• Uniform spectral properties of one-dimensional quasicrystals, II. The Lyapunov exponent (with David Damanik), Lett. Math, Phys. 50 (1999), 245-257. (arXiv:math-ph/9905008)Externer Link
  
  
• Uniform spectral properties of one-dimensional quasicrystals, I. Absence of eigenvalues (with David Damanik), Commun. Math. Phys. 207 (1999), 687-696. (arXiv:math-ph/9903011)Externer Link
  
  
• Hierarchical structures in Sturmian dynamical Systems, preprint 1999, revised version 2001, Theoret. Comput. Sci. 303 (2003).
  
  
• Random Operators and Crossed Products, Mathematical Physics, Analysis and Geometry, 2 (1999), 197-220. (arXiv:math-ph/9902030)Externer Link

Supervision of dissertational projects - Daniel Lenz

• Ian Zimmermann:  Topic concerning non-linear equations.
• Oleksiy Sukaylo:  Topic concering boundaries of graphs.
• Simon Puchert: Topic concerning  harmonic functions.
• Franziska Sieron: Topic in the field of low complexity subshifts.
• Michael Schwartz: Nodal Domains and Boundary Representation for Dirichlet Forms, PhD University of Potsdam,  December 2020; joint supervision with Matthias Keller. 
• Melchior Wirth: Enropic gradient flow structure of quantum Markov semigroups, University of Jena, March 2020.
• Daniel Sell:  Simple Toeplitz subshifts: combinatorial properties and  uniformity of cocycles,  University of Jena, March 2020.
• Christian Oertel:  On dynamical properties of quasicrystals, 2019;  joint supervision with Tobias Jäger. 
• Florentin Münch: Dircrete Ricci curvature, diameter bounds´and rigigity, University Potsdam, December 2019, joint supervision with Matthias Keller, Potsdam. 
• Marcel Schmidt: Energy forms, Friedrich-Schiller-Universität Jena, May 2017.
• Siegfried Beckus:  Spectral approximation of periodic Schr\"odinger Operators, Friedrich-Schiller-Universität Jena, October 2016
• Felix Pogorzelski: Banach-space valued ergodic theorems and spectral approximation, Friedrich-Schiller-Universität Jena,  October 2014.
• Sebastian Haeseler: Analysis of Dirichlet forms on graphs, Friedrich-Schiller-Universität Jena, November 2013.
• Daniel Wingert, "Evolutionsgleichungen und obere Abschätzungen an die Lösungen des Anfangswertproblems",  TU Chemnitz, Juli 2012; joint supervision with Prof. Dr. Peter Stollmann, TU Chemnitz.
• Carsten Schubert: "Quantengraphen mit zufälligem Potential', TU Chemnitz, December 2011; joint supervision with Prof. Dr. Peter Stollmann, TU Chemnitz.
• Matthias Keller: "On the spectral theory of operators on trees", Friedrich-Schiller Universität Jena, December  2010.
• Adnene Besbes: "Ergodic theorems on aperiodic tilings and applications",  Universite Paris 7, July 2008; joint supervision with Prof. Dr. A. Boutet de Monvel, Universite Paris 7.
• Steffen Klassert: "Random operators on Delone sets", TU Chemnitz,  May 2007;  joint supervision with Prof. Dr. P. Stollmann, TU Chemnitz.

Supervision of Master theses:

• Marta Imke: Weyl almost periodic systems in aperiodic order,   March 2026.
• Felix Seifert: Spectral theory of unitary representations of locally compact abelian groups, November 2024.
• Niklas Merk: On Vanishing Entropy of Mean Equicontinuous Dynamical Systems, April 2022.
• Ian Zimmermann: On blow-up of solutions for an abstract semilinear parabolic equation, August 2019.
• Oleksiy Sukaylo: Boundaries of hyperbolic graphs, May 2019.
• Simon Puchert: Resolvable graphs and harmonic functions, Juni 2019.
• Sebastian Uschmann: Kohomologie von Dirichletformen, December 2018.
• Fransiska Sieron: The density of periodic configurations in strongly irreducible subshifts of finite type,  February 2017.
• Michael Schwarz: Boundary representations of Dirichlet forms on discrete spaces, November 2015.
• Jannis Koberstein: Surjectivity of graph Laplacians, November 2015.
• Melchior Wirth:  Uniqueness of form extensions and domination of semigroups, October 2015.
• Daniel Sell: Topological groupoids and Matuis spatial realization theorem, September 2015.
• Florentin Münch: Li-Yau inequalities on finite graphs, November 2014, (joint supervision with Dr. M. Keller).

Supervision of Diploma theses:

• Siegfried Beckus,  "Generalized Bloch Theory for Quasicrystals", Diplom Maerz 2012.
• Marcel Schmidt, "Global properties of Dirichlet forms on discrete spaces", Diplom October 2011.
• Felix Pogorzelski, "Ergodic Theorems on amenable groups", September 2010,  (joint supervision with Prof. Dr. R. Nagel).
• Carsten Schubert, "Laplace-Operatoren auf Quantengraphen", Diplom December 2006, (joint supervision with Prof. Dr. P. Stollmann).
• Matthias Keller, "Produkte zufälliger Matrizen und der Lyapunov-Exponent", Diplom June 2006, (joint supervision with Prof. Dr. P. Stollmann).