TY - GEN
AB - We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.
AU - Schütte, Philipp
AU - Weich, Tobias
AU - Delarue, Benjamin
ID - 31058
TI - Resonances and weighted zeta functions for obstacle scattering via smooth models
ER -
TY - GEN
AU - Hoffmann, Max
ID - 31385
T2 - Mathematische Semesterberichte
TI - Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie
VL - 68
ER -
TY - CHAP
AU - Hoffmann, Max
ED - Biehler, Rolf
ED - Eichler, Andreas
ED - Hochmuth, Reinhard
ED - Rach, Stefanie
ED - Schaper, Niclas
ID - 31364
SN - 2197-8751
T2 - Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert
TI - Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn
ER -
TY - JOUR
AB - Abstract
For a compact Riemannian locally symmetric space $\mathcal M$ of rank 1 and an associated vector bundle $\mathbf V_{\tau }$ over the unit cosphere bundle $S^{\ast }\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\mathbf V_{\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\ast }\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\sigma )$ on compatible associated vector bundles $\mathbf W_{\sigma }$ over $\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\tau$ and $\sigma$ defining the bundles $\mathbf V_{\tau }$ and $\mathbf W_{\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\mathbf W_{\sigma }$. Our methods of proof are based on representation theory and Lie theory.
AU - Küster, Benjamin
AU - Weich, Tobias
ID - 31261
IS - 11
JF - International Mathematics Research Notices
KW - General Mathematics
SN - 1073-7928
TI - Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces
VL - 2021
ER -
TY - JOUR
AU - Häsel-Weide, Uta
AU - Nührenbürger, Marcus
ID - 31576
IS - 14
JF - Zeitschrift für Grundschulforschung (ZfG)
TI - Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.
ER -
TY - JOUR
AU - Häsel-Weide, Uta
AU - Schöttler, Christian
ID - 31577
IS - 2
JF - Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP)
SN - 2701-9012
TI - Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen
ER -
TY - JOUR
AU - Li, Jiaao
AU - Ma, Yulai
AU - Shi, Yongtang
AU - Wang, Weifan
AU - Wu, Yezhou
ID - 32810
JF - European Journal of Combinatorics
KW - Discrete Mathematics and Combinatorics
SN - 0195-6698
TI - On 3-flow-critical graphs
VL - 100
ER -
TY - JOUR
AB - The kinetic Brownian motion on the sphere bundle of a Riemannian manifold M is a stochastic process that models a random perturbation of the geodesic flow. If M is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the L2-spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold.
AU - Kolb, Martin
AU - Weich, Tobias
AU - Wolf, Lasse
ID - 33278
IS - 4
JF - Annales Henri Poincaré
TI - Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature
VL - 23
ER -
TY - GEN
AU - Weich, Tobias
AU - Budde, Julia
ID - 32099
T2 - arXiv:2103.02968v1
TI - Wave Front Sets of Nilpotent Lie Group Representations
ER -
TY - JOUR
AB - While 2D Gibbsian particle systems might exhibit orientational order resulting in a lattice-like structure, these particle systems do not exhibit positional order if the interaction between particles satisfies some weak assumptions. Here we investigate to which extent particles within a box of size may fluctuate from their ideal lattice position. We show that particles near the center of the box typically show a displacement at least of order . Thus we extend recent results on the hard disk model to particle systems with fairly arbitrary particle spins and interaction. Our result applies to models such as rather general continuum Potts type models, e.g. with Widom–Rowlinson or Lenard-Jones-type interaction.
AU - Richthammer, Thomas
AU - Fiedler, Michael
ID - 33481
JF - Stochastic Processes and their Applications
TI - A lower bound on the displacement of particles in 2D Gibbsian particle systems
VL - 132
ER -
TY - JOUR
AU - Hanusch, Maximilian
ID - 34818
JF - Differential Geometry and its Applications
KW - Geometry and Topology
KW - Analysis
SN - 0926-2245
TI - Symmetries of analytic curves
VL - 74
ER -
TY - CHAP
AU - Biehler, Rolf
ED - Biehler, Rolf
ED - Eichler, Andreas
ED - Hochmuth, Reinhard
ED - Rach, Stefanie
ED - Schaper, Niclas
ID - 35720
T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik
TI - Mathematikvorkurse als Brücke in das Studium–Einführung
ER -
TY - CHAP
AU - Biehler, Rolf
AU - Eichler, Andreas
AU - Hochmuth, Reinhard
AU - Rach, Stefanie
AU - Schaper, Niclas
ED - Biehler, Rolf
ED - Eichler, Andreas
ED - Hochmuth, Reinhard
ED - Rach, Stefanie
ED - Schaper, Niclas
ID - 35730
SN - 2197-8751
T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik
TI - Einführung: Lehrinnovationen in der Hochschulmathematik – praxisrelevant – didaktisch fundiert – forschungsbasiert
ER -
TY - JOUR
AU - Biehler, Rolf
AU - Fleischer, Yannik
ID - 35737
JF - Teaching Statistics
KW - Education
KW - Statistics and Probability
SN - 0141-982X
TI - Introducing students to machine learning with decision trees using CODAP and Jupyter Notebooks
VL - 43
ER -
TY - BOOK
ED - Biehler, Rolf
ED - Eichler, Andreas
ED - Hochmuth, Reinhard
ED - Rach, Stefanie
ED - Schaper, Niclas
ID - 35734
SN - 2197-8751
TI - Lehrinnovationen in der Hochschulmathematik
ER -
TY - CHAP
AU - Frischemeier, Daniel
AU - Podworny, Susanne
AU - Biehler, Rolf
ED - Biehler, Rolf
ED - Eichler, Andreas
ED - Hochmuth, Reinhard
ED - Rach, Stefanie
ED - Schaper, Niclas
ID - 35752
SN - 2197-8751
T2 - Konzepte und Studien Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematikzur Hochschuldidaktik und Lehrerbildung Mathematik
TI - Integration fachwissenschaftlicher und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“
ER -
TY - CHAP
AU - Fleischmann, Yael
AU - Biehler, Rolf
AU - Gold, Alexander
AU - Mai, Tobias
ED - Biehler, Rolf
ED - Eichler, Andreas
ED - Hochmuth, Reinhard
ED - Rach, Stefanie
ED - Schaper, Niclas
ID - 35746
SN - 2197-8751
T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik
TI - Integration digitaler Lernmaterialien in die Präsenzlehre am Beispiel des Mathematikvorkurses für Ingenieure an der Universität Paderborn
ER -
TY - JOUR
AU - Frischemeier, Daniel
AU - Biehler, Rolf
AU - Podworny, Susanne
AU - Budde, Lea
ID - 35751
IS - S1
JF - Teaching Statistics
KW - Education
KW - Statistics and Probability
SN - 0141-982X
TI - A first introduction to data science education in secondary schools: Teaching and learning about data exploration withCODAPusing survey data
VL - 43
ER -
TY - JOUR
AU - Biehler, Rolf
AU - Weigand, Hans-Georg
ID - 35744
IS - 228
JF - mathematik lehren
TI - 3D-Geometrie–virtuell und real
VL - 2021
ER -
TY - CHAP
AU - Hochmuth, Reinhard
AU - Biehler, Rolf
AU - Blum, Werner
AU - Achmetli, Kay
AU - Rode, Jana
AU - Krawitz, Janina
AU - Schukajlow, Stanislaw
AU - Bender, Peter
AU - Haase, Jürgen
ED - Biehler, Rolf
ED - Eichler, Andreas
ED - Hochmuth, Reinhard
ED - Rach, Stefanie
ED - Schaper, Niclas
ID - 35757
SN - 2197-8751
T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik
TI - Fachwissen zur Arithmetik bei Grundschullehramtsstudierenden – Entwicklung im ersten Semester und Veränderungen durch eine Lehrinnovation
ER -