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 -