Research
Research Topics
- Complex Geometry and Dynamics
- Riemann Surfaces and Kleinian Groups
- Poincaré Exponents for non-amenable group extensions
- Conformal Measures
- Julia Sets
- Teichmüller Theory
- Non-Commutative Geometry
- Spectral Triples for Fractal Sets
- C*-Algebras and Fractal Geometry
- Finite and Infinte Ergodic Theory
- Thermodynamic Formalism
- Renewal Theory
- Stochastic Analysis of Dynamical Systems
- Limit Laws
- Large Deviations
- Poisson Laws
- Extreme Value Statisitcs
- Fractal Geometry
- Harmonic Analysis on Fractal Sets
- Quantization Dimensions
- Multifractals
- Curvature Measures
- Minkowski Content
- Number Theory
- Diophantine Approximations
- Metrical Theory of Continued Fractions
- Homology for Modular Groups
PhD Dissertations
- Optimal Partition Problems and Applications to Kreĭn-Feller Operators and Quantization Problems / Aljoscha Niemann (2022, Bremen)
- Finite and Infinite Rotation Sequences and Beyond / Arne Mosbach (2019, Bremen)
- Regularity of Aperiodic Subshifts and Connections to Intermediate beta-Transformations / Malte Steffens (2018, Bremen)
- A Study of Measure-Geometric Laplacians on the Real Line / Hendrik Weyer (2018, Bremen)
- Statistics of Rare Events in Infinite Ergodic Theory / Johannes Kautzsch (2015, Bremen)
- Generalized Strong Laws of Large Numbers for Intermediately Trimmed Sums for Non-negative Stationary Processes / Tanja Schindler (2015, Bremen)
- Über Ausströmraten spezieller Flüsse / Fabian Dreher (2015, Bremen)
- AIS message extraction from overlapped AIS signals for SAT-AIS applications / Andis Dembovskis (2015, Bremen - Cooperation DLR)
- Fractal Curvature Measures and Minkowski Content for Limit Sets of Conformal Function Systems / Sabrina Kombrink (2011, Bremen)
- Wavelet and Fourier bases on fractals / Jana Bohnstengel (2011, Bremen)
- Thermodynamic Formalism for Group-Extended Markov Systems with Applications to Fuchsian Groups / Johannes Jaerisch (2011, Bremen)
- Gleichgewichts- und Gibbs-Maße für zelluläre Automaten / Thomas d'Hénin (2009, Bremen)
- Distributionale Konvergenzsätze in unendlicher Ergodentheorie / Mehdi Slassi (2006, Bremen)
- Quantization for probability measures / Zhu, Sanguo (2005, Bremen)
Current PhD Projects
- Lidong Tang: Large Deviations in Infinite Ergodic Theory
- Jakob Fisahn: Dynamics of multiple inducing and applications to metric number theory and geodesic flows
- Chris Moor: Dynamical group extensions and applications to iterated function systems with overlap
- Wafa Ben Saad: Random Fractals and Multifractals with dependence
- Karenina Sender: Diffusion auf irregulären Mengen
- Konstantin Schäfer: Thermodynamischer Formalismus in unendlicher Ergodentheorie
Diplom/Master Theses
- Copulae und assoziierte Markoff-Ketten (2022)
- Dynamische Aspekte von Hidden-Markov-Modellen (2019)
- Markoffsche optimale Stoppstrategien (2019)
- Wartezeiten für Patterns in Zufallsfolgen (2018)
- Quasidiffusionen und Walk Dimension (2018)
- Feature integration with critical dynamics (2018)
- Bestimmung der Hausdorff-Dimension von zufälligen, statistisch selbstähnlichen Cantor-Mengen (2018)
- Eine angepasste Variante von Lins Kriterium und Transferoperator-Methoden (2018)
- The Hausdorff dimension of randomized graphs for Weierstraß functions (2015)
- Diffusion on Nested Fractals (2014)
- Kodierungen Diskreter Hyperebenen mittels Multipler Rotationen (2014)
- On the eigenvalue asymptotic of measure geometric Laplacians on fractals (2014)
- Die Chen-Stein-Methode und Poisson-Gesetze (2012)
- Limit Laws and Trimmed Sums for the Digits of Continued Fractions and Lüroth Series (2011)
- Analyse stochastischer Volatilitätsmodelle mit Hilfe Riemannscher Geometrie (2011)
- Poisson-Approximation via faktorieller Momente (2011)
- Renewal theory for operators in Banach spaces (2011)
- Wavelets on Fractals in ℝ (2009)
- Asymptotische Abweichungen für lange Rückkehrzeiten (2009)
- Exhausting Principles for the Thermodynamic Formalism of Countable State Markov Shifts with Application to Continued Fractions (2008)
Bachelor Theses
- Kombinatorische Eigenschaften von Interval Exchange Transformations (2019)
- Maximierung der Transinformation von Zufallsvariablen mit Nebenbedingungen (2018)
- Die Steinsche Methode zur Poisson-Approximation (2018)
- Diffraktion eindimensionaler Quasikristalle (2018)
- Über einen Satz von Erdős und Kac (2016)
- Das Sekretärinnenproblem (2015)
- Sullivans Beweis vom Riemannschen Abbildungssatz (2015)
Awards
- Sabrina Kombrink received the Bremer Studienpreis 2012 for her PhD dissertation "Fractal Curvature Measures and Minkowski Content for Limit Sets of Conformal Function Systems".
- Johannes Jaerisch received the Bremer Studienpreis 2011 for his PhD dissertation "Thermodynamic Formalism for Group-Extended Markov Systems with Applications to Fuchsian Groups".
- Jana Bohnstengel received the Fachbereichspreis 2009 for Mathematics for her Diplom Thesis "Wavelets on fractals in ℝ ".
- Dr. Mehdi Slassi received an exceptional prize of the Rotary Club Bremen-Roland within the Bremer Studienpreis 2006 for his dissertation "Distributionale Konvergenzsätze in unendlicher Ergodentheorie".
See also Forschungs- und Experteninformationssysteme: Kesseböhmer