@article{31261,
abstract = {{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.}},
author = {{Küster, Benjamin and Weich, Tobias}},
issn = {{1073-7928}},
journal = {{International Mathematics Research Notices}},
keywords = {{General Mathematics}},
number = {{11}},
pages = {{8225--8296}},
publisher = {{Oxford University Press (OUP)}},
title = {{{Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}}},
doi = {{10.1093/imrn/rnz068}},
volume = {{2021}},
year = {{2021}},
}
@article{34818,
author = {{Hanusch, Maximilian}},
issn = {{0926-2245}},
journal = {{Differential Geometry and its Applications}},
keywords = {{Geometry and Topology, Analysis}},
publisher = {{Elsevier BV}},
title = {{{Symmetries of analytic curves}}},
doi = {{10.1016/j.difgeo.2020.101687}},
volume = {{74}},
year = {{2021}},
}
@article{31263,
author = {{Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}},
issn = {{2644-9463}},
journal = {{Annales Henri Lebesgue}},
pages = {{81--119}},
publisher = {{Cellule MathDoc/CEDRAM}},
title = {{{High frequency limits for invariant Ruelle densities}}},
doi = {{10.5802/ahl.67}},
volume = {{4}},
year = {{2021}},
}
@article{36271,
author = {{Brennecken, Dominik and Hilgert, Joachim and Ciardo, Lorenzo}},
journal = {{Journal of Lie Theory}},
number = {{2}},
pages = {{459----468}},
publisher = {{Heldermann Verlag}},
title = {{{Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)}}},
doi = {{10.48550/arXiv.2008.07479}},
volume = {{31}},
year = {{2021}},
}
@misc{51556,
author = {{Hilgert, Joachim}},
booktitle = {{Mathematische Semesterberichte}},
pages = {{171–173}},
title = {{{Philip Ording: 99 Variations on a Proof. Princeton University Press 2019}}},
doi = {{10.1007/s00591-021-00295-7}},
volume = {{68}},
year = {{2021}},
}
@misc{51555,
author = {{Hilgert, Joachim}},
booktitle = {{Mathematische Semesterberichte}},
pages = {{175–177}},
title = {{{Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020}}},
doi = {{10.1007/s00591-021-00296-6}},
volume = {{68}},
year = {{2021}},
}
@article{32006,
author = {{Guillarmou, Colin and Küster, Benjamin}},
issn = {{1424-0637}},
journal = {{Annales Henri Poincaré}},
keywords = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}},
number = {{11}},
pages = {{3565--3617}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds}}},
doi = {{10.1007/s00023-021-01068-7}},
volume = {{22}},
year = {{2021}},
}
@article{35702,
abstract = {{AbstractMathematics Learning Support Centres are becoming more and more common in higher education both internationally and in Germany. Whereas it is clear that their quality largely depends on a functioning interaction in consultations, little is known about how such consultations proceed in detail. On the basis of models from the literature and recorded support sessions (N = 36), we constructed a process model that divides consultations into four ideal–typical phases. In the individual consultations, forward or backward leaps occur, but overall the model seems to describe the data well. A high intercoder reliability shows that it can be applied consistently on real data by different researchers. An analysis of the consultations between students and tutors shows that both mainly work on past attempts or thoughts of the students to solve the exercise or problems and on concrete strategies to solve a problem within the session. In contrast, very little time is dedicated to summarizing and reflecting the solution. The data allows for a more in-depth discussion of what constitutes quality in advising processes and how it might be further explored. Practically, the model may structure support sessions and help in focussing on different goals in different phases.}},
author = {{Schürmann, Mirko and Panse, Anja and Shaikh, Zain and Biehler, Rolf and Schaper, Niclas and Liebendörfer, Michael and Hilgert, Joachim}},
issn = {{2198-9745}},
journal = {{International Journal of Research in Undergraduate Mathematics Education}},
keywords = {{Education, Mathematics (miscellaneous)}},
number = {{1}},
pages = {{94--120}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Consultation Phases in Mathematics Learning and Support Centres}}},
doi = {{10.1007/s40753-021-00154-9}},
volume = {{8}},
year = {{2021}},
}
@book{51493,
author = {{Hilgert, Joachim and Hilgert, Ingrid}},
publisher = {{Springer Spektrum}},
title = {{{Mathematik - Ein Reiseführer 2. Auflage}}},
year = {{2021}},
}
@article{35615,
author = {{Winkler, Michael}},
journal = {{Zeitschrift für Angewandte Mathematik und Physik}},
title = {{{Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes system.}}},
volume = {{72}},
year = {{2021}},
}
@article{35614,
author = {{Winkler, Michael}},
journal = {{International Mathematics Research Notices}},
pages = {{8106--8152}},
title = {{{Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis (-Stokes) systems?}}},
volume = {{2021}},
year = {{2021}},
}
@article{35617,
author = {{Winkler, Michael}},
journal = {{Applied Mathematics Letters}},
pages = {{106785}},
title = {{{Boundedness in a three-dimensional Keller-Segel-Stokes system with subcritical sensitivity.}}},
volume = {{112}},
year = {{2021}},
}
@article{35613,
author = {{Winkler, Michael}},
journal = {{Transactions of the American Mathematical Society}},
pages = {{219--268}},
title = {{{Does spatial homogeneity ultimately prevail in nutrient taxis systems? A paradigm for structure support by rapid diffusion decay in an autonomous parabolic flow.}}},
volume = {{374}},
year = {{2021}},
}
@article{37659,
author = {{Rösler, Margit and Voit, Michael}},
issn = {{0002-9939}},
journal = {{Proceedings of the American Mathematical Society}},
keywords = {{Applied Mathematics, General Mathematics}},
number = {{3}},
pages = {{1151--1163}},
publisher = {{American Mathematical Society (AMS)}},
title = {{{Positive intertwiners for Bessel functions of type B}}},
doi = {{10.1090/proc/15312}},
volume = {{149}},
year = {{2021}},
}
@article{35603,
author = {{Tao, Youshan and Winkler, Michael}},
journal = {{Journal of Functional Analysis}},
title = {{{A fully cross-diffusive two-component evolution system: Existence and qualitative analysis via entropy-consistent thin-film-type approximation.}}},
volume = {{281}},
year = {{2021}},
}
@article{35612,
author = {{Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}},
journal = {{Science China Mathematics}},
pages = {{725--746}},
title = {{{Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption.}}},
volume = {{64}},
year = {{2021}},
}
@article{35605,
author = {{Tao, Youshan and Winkler, Michael}},
journal = {{Communications in Mathematical Sciences}},
pages = {{829--849}},
title = {{{Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime.}}},
volume = {{19}},
year = {{2021}},
}
@article{35610,
author = {{Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}},
journal = {{Communications in Partial Differential Equations}},
pages = {{1058--1091}},
title = {{{Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary.}}},
volume = {{46}},
year = {{2021}},
}
@article{35611,
author = {{Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}},
journal = {{Advances in Nonlinear Analysis}},
pages = {{707--731}},
title = {{{Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation}}},
volume = {{10}},
year = {{2021}},
}
@article{34673,
author = {{Black, Tobias and Fuest, Mario and Lankeit, Johannes}},
issn = {{0044-2275}},
journal = {{Zeitschrift für angewandte Mathematik und Physik}},
keywords = {{Applied Mathematics, General Physics and Astronomy, General Mathematics}},
number = {{3}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems}}},
doi = {{10.1007/s00033-021-01524-8}},
volume = {{72}},
year = {{2021}},
}