Research interests
- Spectral theory of random Schrödinger operators
- Spectral and geometric properties of non-positively curved graphs
- Dirichlet forms and unbounded operators on graphs
Current position
wissenschaftlicher Mitarbeiter (Research associate)
Friedrich Schiller Universität Jena
Teaching this semester
Anwendungen von Operatortheorie - Diskrete Operatoren
Termin: Montag 8:15 (HS 3 Abbeanum); Donnerstag 12:15 (SR 021 August-Bebel-Str.).
Notizen (Es handelt sich nicht um ein Skript zur Vorlesung - Kommentare willkommen)
Preprints
Spectral Analysis of Certain Spherically Homogeneous Graphs
(with Jonathan Breuer), submitted
Volume Growth, Spectrum and Stochastic Completeness of Infinite Graphs
(with Daniel Lenz, Radoslaw K. Wojciechowski), submitted
Note on basic features of large time behaviour of heat kernels
(with Daniel Lenz, Hendrik Vogt, Radoslaw Wojciechowski), submitted
Publications
Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions
(with Sebastian Haeseler, Daniel Lenz, Radoslaw Wojciechowski), to appear in Journal of Spectral theory
Absolutely continuous spectrum for multi-type Galton Watson trees
to appear in Annales Henri Poincaré DOI: 10.1007/s00023-012-0169-9
Absolutely continuous spectrum for random operators on trees of finite cone type
(with Daniel Lenz and Simone Warzel), to appear in Journal d'Analyse Mathematique
On the spectral theory of trees with finite cone type
(with Daniel Lenz and Simone Warzel), to appear in Israel Journal of Mathematics, DOI: 10.1007/s11856-012-0059-3
Curvature, geometry and spectral properties of planar graphs,
Discrete & Computational Geometry: Volume 46, Issue 3 (2011), Page 500-525
Dirichlet forms and stochastic completeness of graphs and subgraphs,
(with Daniel Lenz), to appear in Journal für die reine und angewandte Mathematik (Crelle's Journal), DOI: 10.1515/CRELLE.2011.122
Generalized solutions and spectrum for Dirichlet forms on graphs
(with Sebastian Haeseler), Boundaries and Spectral Theory, Progress in Probability, 2011 Birkhäuser, 181-201.
Cheeger constants, growth and spectrum of locally tessellating planar graphs
(with Norbert Peyerimhoff) Mathematische Zeitschrift, 268, Issue 3-4, (2011), 871-886.
Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation
(with Daniel Lenz), Mathematical Modeling of Natural Phenomena "Spectral Problems" Vol. 5 No. 4 (2010), 198-204.
The essential spectrum of the Laplacian on rapidly branching tessellations,
Mathematische Annalen 346, Issue 1 (2010), 51-66.
PhD thesis
"On the spectral the spectral theory of operators on trees"
or at arxiv.org: here
Diploma thesis
"Produkte zufälliger Matrizen und der Lyapunov-Exponent"
Extended Abstracts
"Absolutely continuous spectrum on trees-random potentials, random
hopping and Galton-Watson trees" Oberwolfach Report No. 50/2011, October 2011
"Curvature and spectrum on graphs" Januar 2012
CV
English version, pdf
Stellen
seit Oktober 2008 (mit Unterbrechung)
wissenschaftlicher Mitarbeiter an der Friedrich Schiller Universität Jena
Februar 2011- Juni 2011
Post Doc an der Hebrew University, Jerusalem, Israel
Oktober 2007 - Mai 2008
Visiting Student Research Collaborator an der Princeton University, USA
Juli 2006 - Juni 2007
wissenschaftlicher Mitarbeiter, TU Chemnitz
Drittmittelstelle des DFG-Projekts "Delone dynamische Systeme: Ergodentheorie, Diffraktion und Operatortheorie"
Ausbildung
Dezember 2010
Promotion in Mathematik, Friedrich Schiller Universität Jena
Juni 2006
Diplom Mathematik mit Nebenfach Physik, TU Chemnitz
Stipendien
Februar 2011 - Juni 2011 Postdoctoral Fellowship am Einstein
Institute of Mathematics, Hebrew University, Jerusalem
Juli 2007 - Juli 2010
Promotionstipendiat der Klaus Murmann Stiftung (sdw)
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Teaching
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| WS 2011/12 |
Übung Analysis III für Mathematiker und Physiker
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| WS 2010/11 |
Übung Analysis I für Mathematiker
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WS 2009/10
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Übung Analysis III für Physiker |
| SS 2009 |
Übung Analysis II für Physiker
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Seminar "Random Schrödinger operators" |
Recent activities
One Day Workshop "Schrödingeroperators" - December 8th 2011 -Friedrich Schiller Universität Jena
Graduate student symposium within the Summer school on "Graphs and spectra" held at the TU Chemnitz in the week 18--23 July 2011, for more information see here
PhD Symposium September 15-16th, Friedrich Schiller University Jena
Talks
Januar 2012, Oberwolfach Mini-Workshop: 'Boundary Value Problems and Spectral Geometry', "Curvature and spectrum on graphs"
December 2011, Jerusalem PDE Seminar, "Absolutely continuous spectrum for Galton Watson trees"
November 2011, TU Claustal "Dirichlet forms on graphs"
October 2011, Oberwolfach Workshop 'Correlations and Interactions for Random Quantum Systems', "Absolutely continuous spectrum on trees"
September 2011, BMS Summer School Berlin 'Random motion and random graphs', "Absolutely continuous spectrum for multi-type Galton Watson trees"
May 2011, Technion Haifa, "On the long time behaviour of heat kernels"
April 2011, Weizmann Institute, Rehovot, "Absolutely continuous spectrum for trees"
March 2011, Hebrew University, Jerusalem, "Curvature and spectrum for graphs"
December 2010, Erlangen University, "Absolutely continuous spectrum for trees"
December 2010, Bielefeld University, "Curvature and spectrum for graphs"
November 2010, Friedrich Schiller University Jena, "Planar graphs of non-positive curvature"
September 2010, Walkshop and PhD Symposium, Jena, "On the spectral theory of trees and tessellations"
September 2010, QMath 11, Hradec Kralove, "Absolutely continuous spectrum for substitution trees"
July 2010, Isaac Newton Institute for Mathematical Sciences Cambridge, Workshop on Analysis on Graphs and its Applications, "Absolutely continuous spectrum for trees of finite forward cone type" (Video)
June 2010, Humboldt University Berlin, "Cheeger constants, exponential growth and spectrum of planar graphs"
June 2010, TU Chemnitz, "Cheeger constants, exponential growth and spectrum of planar graphs"
June 2010, Lausanne CIB, Workshop on Random Schrödinger operators, "Stability of ac spectrum: Contraction properties of the recursion relation"
May 2010, AIMS Conference on Dynamical Systems, Differential Equations and Applications "Stability of ac spectrum under random perturbations on trees"
May 2010, Friedrich Schiller University Jena, "Discrete Spectrum for Schrödinger operators on graphs"
January 2010, Friedrich Schiller University Jena, "Cheegerkonstanten, exponentielles Wachstum und Spektrum von planaren Graphen"
November 2009, University of Lisbon, Group of Mathematical Physics, "Cheeger constants, exponential growth and spectrum of planar graphs"
October 2009, Hebrew University Jerusalem, "Trees of finite vertex type and absolutely continuous spectrum"
September 2009, TU Chemnitz Graphs, Quantum Graphs and their Spectra + Walkshop 2009, "Dirichlet forms on discrete sets and absence of essential spectrum"
July 2009, Blaubeuren, "Workshop on Structure and Dynamics of Networks": "Heat transport to the boundary on discrete graphs"
July 2009, St. Kathrein, "Alp-Workshop": "Random trees and absolutely continuous spectrum"
June 2009, Graz, "Workshop on Boundaries": "Heat transport to the boundary"
December 2008, Bielefeld University, Seminar "Mathematik in den Naturwissenschaften" (SFB): "The Laplacian on rapidly branching Graphs"
November 2008, Graz University "Mathematische Strukturtheorie", "The Laplacian on rapidly branching graphs"
November 2008, ESI Vienna, Workshop "Structural Probability", "The Laplacian (plus potential) on trees and rapidly branching graphs"
November 2008, University of Vienna, Seminar Analysis, "The Laplacian on rapidly branching graphs"
October 2008, LMU Munich, Seminar "Analysis und Zufall", "The Laplacian on rapidly branching graphs"
April 2008, Houston Rice University, Geometry-Analysis Seminar , "The Laplacian on rapidly branching graphs"
February 2008, Graduate Center CUNY, NY, Differential Geometry Seminar, "The Laplacian on rapidly branching graphs"
September 2007, Durham University, Geometry Seminar, "Spectral properties of rapidly branching graphs"
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