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 -