Mathematisches Institut
Neues Augusteum A 431
Augustusplatz 10
04109 Leipzig
E-Mail: firstname.lastname@math.uni-leipzig.de
Phone: +49-341-97-32148
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Mathematisches Institut 04109 Leipzig E-Mail: firstname.lastname@math.uni-leipzig.de Phone: +49-341-97-32148 |
| since 2023: | Professor for Analysis II, Universität Leipzig |
| 2017-2023: | Felix-Klein-Juniorprofessor (tenure-track) for Mathematics, Universität Leipzig |
| 2014-2017: | Post-Doctoral Research Fellow, Technion Haifa (IL) |
| 2011-2014: | Doctoral studies in mathematics, Friedrich-Schiller-Universität Jena |
| 2007-2008: | Visiting student, Princeton University (USA) |
| 2005-2010: | Diploma studies in mathematics, Eberhard-Karls-Universität Tübingen |
"Spectral approximation for substitution systems"
(with Ram Band, Siegfried Beckus and Lior Tenenbaum)
"Strictly irreducible Markov shifts and ergodicity of skew-product extensions"
(with Pablo Lummerzheim and Elias Zimmermann, submitted)
"Symbolic substitution systems beyond abelian groups"
(with Siegfried Beckus and Tobias Hartnick, submitted)
"Linear repetitivity beyond abelian groups"
(with Siegfried Beckus and Tobias Hartnick, submitted)
"Agmon estimates for Schrödinger operators on graphs"
(with Matthias Keller, to appear in J. Ana. Math. 2024)
"Shannon-McMillan-Breiman theorem along almost geodesics in negatively curved groups"
(with Amos Nevo, J. Theo. Prob. 37 (1), pp. 814-859, 2024)
"An improved discrete p-Hardy inequality"
(with Florian Fischer and Matthias Keller, Int. Eq. Oper. Th. 95 (4), 17 pp., 2023)
"Leptin densities in amenable groups"
(with Christoph Richard and Nicolae Strungaru, J. Fourier Ana. Appl. 28 (6), 36 pp., 2022)
"Aperiodic order and spherical diffraction, III: The shadow transform and the diffraction formula"
(with Michael Björklund and Tobias Hartnick, J. Funct. Ana. 281 (12), 59 pp., 2021)
"The Shannon-McMillan-Breiman theorem beyond amenable groups"
(with Amos Nevo, Illinois J. Math. 65 (4), pp. 869-905, 2021)
"Aperiodic order and spherical diffraction, II: Translation bounded measures on homogeneous spaces"
(with Michael Björklund and Tobias Hartnick, Math. Zeitschr. 300 (2), pp. 1157-1201, 2022)
"From Hardy to Rellich inequalities on graphs"
(with Matthias Keller and Yehuda Pinchover, Proc. Lond. Math. Soc. 122 (3), pp. 458-477, 2021)
"Delone dynamical systems and spectral convergence"
(with Siegfried Beckus, Ergod. Th. Dyn. Sys. 40 (6), pp. 1510-1544, 2020)
"Criticality theory for Schrödinger operators on graphs"
(with Matthias Keller, Yehuda Pinchover, J. Spectral Theory 10 (1), pp. 73-114, 2020)
"The Ihara Zeta function for infinite graphs"
(with Daniel Lenz and Marcel Schmidt, Trans. Amer. Math. Soc. 371 (8), pp. 5687-5729, 2019)
"An improved discrete Hardy inequality"
(with Matthias Keller,
Yehuda Pinchover, Amer. Math. Monthly 125 (4), pp. 347-350, 2018)
"Optimal Hardy inequalities for Schrödinger operators on graphs"
(with Matthias Keller and Yehuda Pinchover, Comm. Math. Phys. 358 (2), pp. 767-790, 2018)
"Aperiodic order and spherical diffraction, I: Auto-correlation of model sets"
(with Michael Björklund and Tobias Hartnick, Proc. Lond. Math. Soc. 116 (4), pp. 957-996, 2018)
"Diffusion on Delone sets"
(with Sebastian Haeseler, Xueping Huang and Daniel Lenz, J. Stat. Phys. 167 (6), pp. 1496-1510, 2017)
"Geometry and spectrum of rapidly branching graphs"
(with Matthias Keller and Florentin Münch,
Math. Nachr. 289 (13), pp. 1636-1647, 2016)
"Sectional curvature of polygonal complexes with planar substructures"
(with Matthias Keller and Norbert Peyerimhoff, Adv. in Math. 307, pp. 1070-1107, 2017)
"Convergence theorems for graph sequences"
(Int. J. Algebra Comput. 24 (8), 2014)
"A Banach-space valued ergodic theorem for amenable groups and applications"
(with Fabian Schwarzenberger, J. d'Anal. Math. 130 (1), pp. 19-69, 2016)
"Spectrum of Lebesgue measure zero for Jacobi operators of quasicrystals"
(with Siegfried Beckus, Mathematical Physics, Analysis and Geometry 16 (3), pp. 289-308, 2013)
"Almost-additive ergodic theorems for amenable groups"
(J. Funct. Ana. 265 (8), pp. 1615-1666, 2013)
Addendum and Corrigendum
"Uniform existence of the integrated density of states on metric Cayley graphs"
(with Fabian Schwarzenberger and Christian Seifert, Lett. Math. Phy. 103 (9), pp. 1009-1028, 2013)
"Symbolic substitutions in dilation groups"
MFO report for workshop 2203 "Groups and Dynamics: Topology, Measure, and Borel Structure", 2022, to appear.
"Critical Hardy inequalities on manifolds and graphs"
(with Matthias Keller, Yehuda Pinchover)
Peer reviewed proceedings ``Analysis and Geometry on Graphs and Ganifolds''
(edited by Matthias Keller, Daniel Lenz and Radoslaw K. Wojciechowski),
LMS Lec. Not. Ser. 461, Cambridge U. Press, 2020
"Quasicrystals beyond amenable groups"
(with Tobias Hartnick)
MFO report workshop "Spectral and Topological Methods in Mathematical Quasicrystals", No. 46/2017, pp. 2809-2813
"Subadditive convergence and cocycle entropy"
MFO report workshop "Measured group theory", No. 41/2016, pp. 2382-2384
"Diffraction I"
MFO report Arbeitsgemeinschaft ``Mathematical Quasicrystals'', No. 44/2015, pp. 2620-2622
"Banach space-valued ergodic theorems and spectral approximation", pdf
"Ergodic theorems on amenable groups", pdf
05/2024 University of Oslo (N), Workshop ``Point sets: Dynamics, Sampling, and Operator Algebras'': Symbolic substitutions and spectral convergence''
03/2024 University of Leipzig, Conference ``Aspects of Ergodic Theory for Hyperbolic groups'': "On entropy equipartition beyond amenable groups"
01/2024 MPI-MIS Leipzig: "Entropy equipartition along almost geodesics in negatively curved groups"
08/2023 Oberwolfach MFO, Workshop 2335 Aspects of Aperiodic Order: "Symbolic substitutions in the Heisenberg group and spectral approximation"
06/2023 Technion (IL), PDE seminar: "Symbolic substitutions in the Heisenberg group and spectral approximation"
06/2023 Technion (IL), GDRT seminar: "Entropy equipartition along almost geodesics in negatively curved groups"
05/2023 Technion (IL), Pizza seminar: "An improved p-Hardy inequality on the half line"
03/2023 Rutgers University (USA), online ETA seminar: "Symbolic substitutions beyond abelian groups"
01/2023 University of Paderborn, Harish-Chandra seminar: "Aperiodic order beyond abelian groups"
10/2022 University of Kiel, 10th Workshop "Operator Theoretic Aspects of Ergodic Theory": "Entropy equipartition along almost geodesics in negatively curved groups"
01/2022 MFO Oberwolfach, Workshop "Groups and Dynamics: Topology, Measure, and Borel Structure": "Symbolic substitutions for dilation groups"
11/2021 Lecture for high school students, Gymnasium St. Augustin Grimma: "Ordnung in mathematischen Strukturen - schwer zu finden, schwer zu vermeiden" (in German)
11/2020 TU Dortmund, online seminar: "Mathematical quasicrystals and unique ergodicity"
11/2020 University of Maryland (USA), online seminar: "Linear repetitive Delone sets beyond Abelian groups"
02/2020 University of Potsdam, Colloquium: "What is a quasicrystal?"
12/2019 University of Leipzig, 1st VISTA seminar: "Certain uncertainties and discrete Hardy inequalities"
10/2019 University of Science and Technology, Wroclaw (PL): "On the Shannon-McMillan-Breiman theorem
beyond amenable groups"
07/2019 Jagellonian University, Krakow (PL): "On non-commutative quasicrystals"
04/2019 Ben Gurion University, Beer-Sheva (IL): "New developments on non-commutative quasicrystals"
09/2018 Conference "Groups, Spectral and L2-Invariants", Geneva (CH): "Approximation of spectral measures"
09/2018 Conference "Model Sets and Aperiodic Order", Durham (UK): "Approximation of spectral measures"
08/2018 Leipziger Schülergesellschaft für Mathematik (LSGM), Festvortrag Schuljahr 2018/19: "Echte Daten und Kreisdrehungen"
03/2018 Technion Haifa (IL): "On spectral approximation on Delone sets"
03/2018 Workshop "Quasicrystals, Delone sets and Generalizations of Lattices", Ohalo (IL): "Delone sets on groups - an introduction"
02/2018 Bernoulli center (CIB), EPFL Lausanne, Conference "Borel combinatorics and ergodic theory": "The Ihara zeta function for measured graphs"
12/2017 University of Leipzig, "52nd Seminar Sophus Lie: "Quasicrystals beyond abelian groups"
11/2017 University of Tuebingen, 5th Workshop "Operator Theoretic Aspects of Ergodic Theory": "On the dynamics of non-commutative quasicrystals"
11/2017 Leipzig, Max-Planck Institute for Mathematics in the Sciences: "Optimal Hardy weights on graphs"
10/2017 MFO Oberwolfach, Workshop "Spectral and Topological Methods in Mathematical Quasicrystals": "Quasicrystals beyond amenable groups"
08/2017 Conference "Analysis and Geometry on Graphs and Manifolds", Potsdam: "Optimal Hardy inequalities on graphs"
07/2017 Banff International Research Station (CA), Workshop "Mean dimension and sofic entropy meet dynamical systems": "Subadditive convergence via measured equivalence relations"
06/2017 Texas A& M University (USA), Conference "Ergodic theory and operator algebras": "The Shannon-McMillan-Breiman theorem beyond amenable groups"
12/2016 KIT Karlsruhe: "Borel equivalence relations and subadditive convergence"
12/2016 KIT Karlsruhe, RTG Colloquium: "On entropy theory for non-amenable groups"
11/2016 Technion Haifa (IL), Colloquium Talk: "On cocycle entropy"
09/2016 MFO Oberwolfach, Conference "Measured Group Theory": "Subadditive convergence and cocycle entropy"
08/2016 University of Tübingen: "Kozykel Entropie"
06/2016 University of Leipzig: "Nichtkommutative Quasikristalle"
06/2016 University of Erlangen: "Non-commutative quasicrystals"
06/2016 University of Jena: "Non-commutative quasicrystals", two talks
06/2016 Dresden University of Technology: "On non-commutative quasicrystals"
06/2016 Israel Mathematical Union Annual Meeting (IL): "Non-commutative quasicrystals"
05/2016 Tel Aviv University (IL): "Non-commutative quasicrystals"
02/2016 Conference "Measured group theory", ESI Vienna: "Ihara's zeta function for measured graphs"
01/2016 University of Potsdam : "Taking the mean in groups without a mean"
11/2015 University of Potsdam: "News about entropy"
11/2015 University of Jena: "Towards quasicrystals in non-commutative spaces"
11/2015 University of Jena: "News about entropy"
10/2015 Technion Haifa (IL): "Quasicrystals and dynamical systems"
10/2015 MFO Oberwolfach, Arbeitsgemeinschaft "Mathematical Quasicrystals": Talk "Diffraction I"
06/2015 Tel Aviv University (IL): "Towards quasicrystals in non-commutative spaces"
06/2015 University of Haifa (IL), Colloqium: "Polygonal complexes and non-positive planar sectional curvature"
12/2014 Hebrew University, Jerusalem (IL): "A Banach space-valued ergodic theorem for amenable groups"
11/2014 Technion Haifa (IL): "Groups and spectral approximation"
08/2014 Chalmers University, Göteborg (S): "Almost-additive ergodic theorems for amenable groups"
05/2014 University of Jena: "Ihara's zeta function for big graphs"
03/2014 Conference "Fractal Geometry and Stochastics V", Tabarz: "The Ihara zeta function for infinite graphs"
03/2014 Universität Halle, Konferenz "Grüppchen": "Gruppen und Ergodensätze"
03/2014 Leipzig, Max-Planck Institute for Mathematics in the Sciences: "Ergodic theorems for almost-additive functions"
01/2014 Drei-Städte-Seminar, University of Leipzig: "Konvergenz diskreter Geometrien und spektrale Approximation"
01/2014 Chemnitz University of Technology: "Punktweise Ergodensätze für die freie Gruppe - der Ansatz von Bowen und Nevo"
11/2013 University of Hamburg: "Convergence theorems for graph sequences"
09/2013 Conference "Geometric and Analytic Group Theory", Ventotene (IT): "Graphs and spectral approximation"
07/2013 University of Leipzig: "Convergence theorems for graph sequences"
07/2013 University of Jena: "Graphs and spectral approximation"
05/2013 Eötvös Loránd University, Budapest (H): "Graphs and (non-)amenability"
01/2013 University of Jena: "Convergence theorems for graph sequences"
01/2013 Chemnitz University of Technology: "Convergence theorems for graph sequences"
12/2012 Center for Mathematics Modeling (CMM Universidad de Chile), Santiago de Chile (CL):
"An almost-additive ergodic theorem on amenable groups"
11/2012 Catholic University of Valparaíso (CL): "Almost-additive ergodic theorems on amenable groups"
10/2012 Hamburg-Harburg University of Technology: "Ergodic theorems and integrated density of states"
06/2012 University of Erlangen-Nürnberg (FAU Erlangen): "Fast-additive Ergodensätze für mittelbare Gruppen"
05/2012 Leipzig, Max-Planck Institute for Mathematics in the Sciences: "The existence of the integrated density
of states on amenable Cayley graphs"
01/2012 Chemnitz University of Technology: "A Banach space valued ergodic theorem for amenable groups"
07/2011 Chemnitz University of Technology: "The integrated density of states on amenable graphs",
(Summer School "Graphs and Spectra")
06/2010 Kacov (CZ): "The Euler formula for strongly continuous semigroups",
(13th TULKA Internet Seminar 'Gradient Systems')
05/2010 Delft University of Technology (NL): "Ergodic theorems on amenable groups"
05/2010 Chemnitz University of Technology: "Pointwise ergodic theorems on amenable groups"
06/2009 Blaubeuren: "The ergodic theoretical proof of the Szemeredi theorem",
(12th TULKA Internet Seminar 'Ergodic Theory')