[{"language":[{"iso":"eng"}],"article_number":"45","doi":"10.1007/s00220-024-05226-w","publication_identifier":{"issn":["0010-3616","1432-0916"]},"author":[{"last_name":"Janssens","first_name":"Bas","full_name":"Janssens, Bas"},{"full_name":"Niestijl, Milan","first_name":"Milan","last_name":"Niestijl"}],"year":"2025","title":"Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms","intvolume":"       406","date_updated":"2026-02-20T09:41:41Z","publication_status":"published","date_created":"2026-02-20T09:33:11Z","department":[{"_id":"93"}],"type":"journal_article","issue":"2","publication":"Communications in Mathematical Physics","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>Motivated by asymptotic symmetry groups in general relativity, we consider projective unitary representations <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$\\overline{\\rho }$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mover>\r\n                    <mml:mi>ρ</mml:mi>\r\n                    <mml:mo>¯</mml:mo>\r\n                  </mml:mover>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula> of the Lie group <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$${{\\,\\textrm{Diff}\\,}}_c(M)$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:msub>\r\n                      <mml:mrow>\r\n                        <mml:mspace/>\r\n                        <mml:mtext>Diff</mml:mtext>\r\n                        <mml:mspace/>\r\n                      </mml:mrow>\r\n                      <mml:mi>c</mml:mi>\r\n                    </mml:msub>\r\n                    <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:mi>M</mml:mi>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula> of compactly supported diffeomorphisms of a smooth manifold <jats:italic>M</jats:italic> that satisfy a so-called generalized positive energy condition. In particular, this captures representations that are in a suitable sense compatible with a KMS state on the von Neumann algebra generated by <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$\\overline{\\rho }$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mover>\r\n                    <mml:mi>ρ</mml:mi>\r\n                    <mml:mo>¯</mml:mo>\r\n                  </mml:mover>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula>. We show that if <jats:italic>M</jats:italic> is connected and <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$\\dim (M) &gt; 1$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>dim</mml:mo>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mi>M</mml:mi>\r\n                    <mml:mo>)</mml:mo>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>1</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula>, then any such representation is necessarily trivial on the identity component <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$${{\\,\\textrm{Diff}\\,}}_c(M)_0$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:msub>\r\n                      <mml:mrow>\r\n                        <mml:mspace/>\r\n                        <mml:mtext>Diff</mml:mtext>\r\n                        <mml:mspace/>\r\n                      </mml:mrow>\r\n                      <mml:mi>c</mml:mi>\r\n                    </mml:msub>\r\n                    <mml:msub>\r\n                      <mml:mrow>\r\n                        <mml:mo>(</mml:mo>\r\n                        <mml:mi>M</mml:mi>\r\n                        <mml:mo>)</mml:mo>\r\n                      </mml:mrow>\r\n                      <mml:mn>0</mml:mn>\r\n                    </mml:msub>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula>. As an intermediate step towards this result, we determine the continuous second Lie algebra cohomology <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$H^2_\\textrm{ct}(\\mathcal {X}_c(M), \\mathbb {R})$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:msubsup>\r\n                      <mml:mi>H</mml:mi>\r\n                      <mml:mtext>ct</mml:mtext>\r\n                      <mml:mn>2</mml:mn>\r\n                    </mml:msubsup>\r\n                    <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:msub>\r\n                        <mml:mi>X</mml:mi>\r\n                        <mml:mi>c</mml:mi>\r\n                      </mml:msub>\r\n                      <mml:mrow>\r\n                        <mml:mo>(</mml:mo>\r\n                        <mml:mi>M</mml:mi>\r\n                        <mml:mo>)</mml:mo>\r\n                      </mml:mrow>\r\n                      <mml:mo>,</mml:mo>\r\n                      <mml:mi>R</mml:mi>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula> of the Lie algebra of compactly supported vector fields. This is subtly different from Gelfand–Fuks cohomology in view of the compact support condition.</jats:p>","lang":"eng"}],"publisher":"Springer Science and Business Media LLC","_id":"64289","volume":406,"user_id":"104095","status":"public","citation":{"chicago":"Janssens, Bas, and Milan Niestijl. “Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms.” <i>Communications in Mathematical Physics</i> 406, no. 2 (2025). <a href=\"https://doi.org/10.1007/s00220-024-05226-w\">https://doi.org/10.1007/s00220-024-05226-w</a>.","short":"B. Janssens, M. Niestijl, Communications in Mathematical Physics 406 (2025).","apa":"Janssens, B., &#38; Niestijl, M. (2025). Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms. <i>Communications in Mathematical Physics</i>, <i>406</i>(2), Article 45. <a href=\"https://doi.org/10.1007/s00220-024-05226-w\">https://doi.org/10.1007/s00220-024-05226-w</a>","ieee":"B. Janssens and M. Niestijl, “Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms,” <i>Communications in Mathematical Physics</i>, vol. 406, no. 2, Art. no. 45, 2025, doi: <a href=\"https://doi.org/10.1007/s00220-024-05226-w\">10.1007/s00220-024-05226-w</a>.","ama":"Janssens B, Niestijl M. Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms. <i>Communications in Mathematical Physics</i>. 2025;406(2). doi:<a href=\"https://doi.org/10.1007/s00220-024-05226-w\">10.1007/s00220-024-05226-w</a>","bibtex":"@article{Janssens_Niestijl_2025, title={Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms}, volume={406}, DOI={<a href=\"https://doi.org/10.1007/s00220-024-05226-w\">10.1007/s00220-024-05226-w</a>}, number={245}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Janssens, Bas and Niestijl, Milan}, year={2025} }","mla":"Janssens, Bas, and Milan Niestijl. “Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms.” <i>Communications in Mathematical Physics</i>, vol. 406, no. 2, 45, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00220-024-05226-w\">10.1007/s00220-024-05226-w</a>."}},{"user_id":"72064","volume":406,"publisher":"Springer Science and Business Media LLC","_id":"66291","status":"public","citation":{"bibtex":"@article{Burban_Klevtsov_2025, title={Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus}, volume={406}, DOI={<a href=\"https://doi.org/10.1007/s00220-025-05267-9\">10.1007/s00220-025-05267-9</a>}, number={597}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Burban, Igor and Klevtsov, Semyon}, year={2025} }","ama":"Burban I, Klevtsov S. Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus. <i>Communications in Mathematical Physics</i>. 2025;406(5). doi:<a href=\"https://doi.org/10.1007/s00220-025-05267-9\">10.1007/s00220-025-05267-9</a>","mla":"Burban, Igor, and Semyon Klevtsov. “Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus.” <i>Communications in Mathematical Physics</i>, vol. 406, no. 5, 97, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00220-025-05267-9\">10.1007/s00220-025-05267-9</a>.","short":"I. Burban, S. Klevtsov, Communications in Mathematical Physics 406 (2025).","chicago":"Burban, Igor, and Semyon Klevtsov. “Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus.” <i>Communications in Mathematical Physics</i> 406, no. 5 (2025). <a href=\"https://doi.org/10.1007/s00220-025-05267-9\">https://doi.org/10.1007/s00220-025-05267-9</a>.","ieee":"I. Burban and S. Klevtsov, “Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus,” <i>Communications in Mathematical Physics</i>, vol. 406, no. 5, Art. no. 97, 2025, doi: <a href=\"https://doi.org/10.1007/s00220-025-05267-9\">10.1007/s00220-025-05267-9</a>.","apa":"Burban, I., &#38; Klevtsov, S. (2025). Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus. <i>Communications in Mathematical Physics</i>, <i>406</i>(5), Article 97. <a href=\"https://doi.org/10.1007/s00220-025-05267-9\">https://doi.org/10.1007/s00220-025-05267-9</a>"},"doi":"10.1007/s00220-025-05267-9","article_number":"97","language":[{"iso":"eng"}],"date_updated":"2026-07-07T06:18:58Z","publication_status":"published","intvolume":"       406","title":"Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus","year":"2025","author":[{"last_name":"Burban","first_name":"Igor","full_name":"Burban, Igor","id":"72064"},{"last_name":"Klevtsov","first_name":"Semyon","full_name":"Klevtsov, Semyon"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"type":"journal_article","date_created":"2026-07-07T06:18:00Z","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>In 1993 Keski-Vakkuri and Wen introduced a model for the fractional quantum Hall effect based on multilayer two-dimensional electron systems satisfying quasi-periodic boundary conditions. Such a model is essentially specified by a choice of a complex torus <jats:italic>E</jats:italic> and a symmetric positively definite matrix <jats:italic>K</jats:italic> of size <jats:italic>g</jats:italic> with non-negative integral coefficients, satisfying some further constraints. The space of the corresponding wave functions turns out to be <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$\\delta $$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>δ</mml:mi>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula>-dimensional, where <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$\\delta $$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>δ</mml:mi>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula> is the determinant of <jats:italic>K</jats:italic>. We construct a hermitian holomorphic bundle of rank <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$\\delta $$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>δ</mml:mi>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula> on the abelian variety <jats:italic>A</jats:italic> (which is the <jats:italic>g</jats:italic>-fold product of the torus <jats:italic>E</jats:italic> with itself), whose fibres can be identified with the space of wave function of Keski-Vakkuri and Wen. A rigorous construction of this “magnetic bundle” involves the technique of Fourier–Mukai transforms on abelian varieties. The constructed bundle turns out to be simple and semi-homogeneous and it can be equipped with two different (and natural) hermitian metrics: the one coming from the center-of-mass dynamics and the one coming from the Hilbert space of the underlying many-body system. We prove that the canonical Bott–Chern connection of the first hermitian metric is always projectively flat and give sufficient conditions for this property for the second hermitian metric.</jats:p>","lang":"eng"}],"issue":"5","publication":"Communications in Mathematical Physics"},{"user_id":"99427","volume":388,"page":"419-433","_id":"43465","publisher":"Springer Science and Business Media LLC","status":"public","oa":"1","external_id":{"arxiv":["2102.13373"]},"citation":{"mla":"Hasler, David, et al. “On Existence of Ground States in the Spin Boson Model.” <i>Communications in Mathematical Physics</i>, vol. 388, no. 1, Springer Science and Business Media LLC, 2021, pp. 419–33, doi:<a href=\"https://doi.org/10.1007/s00220-021-04185-w\">10.1007/s00220-021-04185-w</a>.","ama":"Hasler D, Hinrichs B, Siebert O. On Existence of Ground States in the Spin Boson Model. <i>Communications in Mathematical Physics</i>. 2021;388(1):419-433. doi:<a href=\"https://doi.org/10.1007/s00220-021-04185-w\">10.1007/s00220-021-04185-w</a>","bibtex":"@article{Hasler_Hinrichs_Siebert_2021, title={On Existence of Ground States in the Spin Boson Model}, volume={388}, DOI={<a href=\"https://doi.org/10.1007/s00220-021-04185-w\">10.1007/s00220-021-04185-w</a>}, number={1}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}, year={2021}, pages={419–433} }","apa":"Hasler, D., Hinrichs, B., &#38; Siebert, O. (2021). On Existence of Ground States in the Spin Boson Model. <i>Communications in Mathematical Physics</i>, <i>388</i>(1), 419–433. <a href=\"https://doi.org/10.1007/s00220-021-04185-w\">https://doi.org/10.1007/s00220-021-04185-w</a>","ieee":"D. Hasler, B. Hinrichs, and O. Siebert, “On Existence of Ground States in the Spin Boson Model,” <i>Communications in Mathematical Physics</i>, vol. 388, no. 1, pp. 419–433, 2021, doi: <a href=\"https://doi.org/10.1007/s00220-021-04185-w\">10.1007/s00220-021-04185-w</a>.","chicago":"Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “On Existence of Ground States in the Spin Boson Model.” <i>Communications in Mathematical Physics</i> 388, no. 1 (2021): 419–33. <a href=\"https://doi.org/10.1007/s00220-021-04185-w\">https://doi.org/10.1007/s00220-021-04185-w</a>.","short":"D. Hasler, B. Hinrichs, O. Siebert, Communications in Mathematical Physics 388 (2021) 419–433."},"doi":"10.1007/s00220-021-04185-w","main_file_link":[{"open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2026-01-16T09:02:44Z","article_type":"original","intvolume":"       388","title":"On Existence of Ground States in the Spin Boson Model","year":"2021","author":[{"full_name":"Hasler, David","last_name":"Hasler","first_name":"David"},{"id":"99427","first_name":"Benjamin","orcid":"0000-0001-9074-1205","last_name":"Hinrichs","full_name":"Hinrichs, Benjamin"},{"first_name":"Oliver","last_name":"Siebert","full_name":"Siebert, Oliver"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"type":"journal_article","date_created":"2023-04-13T18:07:22Z","extern":"1","abstract":[{"lang":"eng","text":"We show the existence of ground states in the massless spin boson model without any infrared regularization. Our proof is non-perturbative and relies on a compactness argument. It works for arbitrary values of the coupling constant under the hypothesis that the second derivative of the ground state energy as a function of a constant external magnetic field is bounded."}],"issue":"1","publication":"Communications in Mathematical Physics"},{"citation":{"mla":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, Springer Science and Business Media LLC, 2020, pp. 917–41, doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>.","bibtex":"@article{Küster_Weich_2020, title={Pollicott-Ruelle Resonant States and Betti Numbers}, volume={378}, DOI={<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Küster, Benjamin and Weich, Tobias}, year={2020}, pages={917–941} }","ama":"Küster B, Weich T. Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>. 2020;378(2):917-941. doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>","ieee":"B. Küster and T. Weich, “Pollicott-Ruelle Resonant States and Betti Numbers,” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, pp. 917–941, 2020, doi: <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>.","apa":"Küster, B., &#38; Weich, T. (2020). Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>, <i>378</i>(2), 917–941. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>","short":"B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.","chicago":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i> 378, no. 2 (2020): 917–41. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>."},"status":"public","_id":"31264","publisher":"Springer Science and Business Media LLC","page":"917-941","volume":378,"user_id":"49178","publication":"Communications in Mathematical Physics","issue":"2","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Given a closed orientable hyperbolic manifold of dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ne 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>≠</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.\r\n</jats:p>","lang":"eng"}],"date_created":"2022-05-17T12:06:06Z","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"author":[{"first_name":"Benjamin","last_name":"Küster","full_name":"Küster, Benjamin"},{"id":"49178","orcid":"0000-0002-9648-6919","first_name":"Tobias","last_name":"Weich","full_name":"Weich, Tobias"}],"year":"2020","title":"Pollicott-Ruelle Resonant States and Betti Numbers","intvolume":"       378","date_updated":"2022-05-19T10:13:48Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1007/s00220-020-03793-2"},{"department":[{"_id":"548"}],"type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"date_created":"2024-04-11T12:33:03Z","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Given a closed orientable hyperbolic manifold of dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ne 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>≠</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.\r\n</jats:p>","lang":"eng"}],"publication":"Communications in Mathematical Physics","issue":"2","doi":"10.1007/s00220-020-03793-2","language":[{"iso":"eng"}],"intvolume":"       378","date_updated":"2024-04-11T12:36:53Z","publication_status":"published","publication_identifier":{"issn":["0010-3616","1432-0916"]},"author":[{"full_name":"Küster, Benjamin","last_name":"Küster","first_name":"Benjamin"},{"id":"49178","orcid":"0000-0002-9648-6919","last_name":"Weich","first_name":"Tobias","full_name":"Weich, Tobias"}],"title":"Pollicott-Ruelle Resonant States and Betti Numbers","year":"2020","citation":{"mla":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, Springer Science and Business Media LLC, 2020, pp. 917–41, doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>.","bibtex":"@article{Küster_Weich_2020, title={Pollicott-Ruelle Resonant States and Betti Numbers}, volume={378}, DOI={<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Küster, Benjamin and Weich, Tobias}, year={2020}, pages={917–941} }","ama":"Küster B, Weich T. Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>. 2020;378(2):917-941. doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>","ieee":"B. Küster and T. Weich, “Pollicott-Ruelle Resonant States and Betti Numbers,” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, pp. 917–941, 2020, doi: <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>.","apa":"Küster, B., &#38; Weich, T. (2020). Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>, <i>378</i>(2), 917–941. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>","short":"B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.","chicago":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i> 378, no. 2 (2020): 917–41. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>."},"volume":378,"user_id":"70575","publisher":"Springer Science and Business Media LLC","_id":"53415","page":"917-941","status":"public"},{"volume":367,"user_id":"31496","doi":"10.1007/s00220-018-3238-1","_id":"63354","publisher":"Springer Science and Business Media LLC","language":[{"iso":"eng"}],"page":"665-681","intvolume":"       367","publication_status":"published","date_updated":"2025-12-19T10:53:03Z","author":[{"full_name":"Souplet, Philippe","first_name":"Philippe","last_name":"Souplet"},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"status":"public","title":"Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions                                                                   $${n\\geq 3}$$                                                                            n                      ≥                      3","year":"2018","type":"journal_article","date_created":"2025-12-19T10:52:55Z","citation":{"mla":"Souplet, Philippe, and Michael Winkler. “Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions                                                                   $${n\\geq 3}$$                                                                            n                      ≥                      3.” <i>Communications in Mathematical Physics</i>, vol. 367, no. 2, Springer Science and Business Media LLC, 2018, pp. 665–81, doi:<a href=\"https://doi.org/10.1007/s00220-018-3238-1\">10.1007/s00220-018-3238-1</a>.","bibtex":"@article{Souplet_Winkler_2018, title={Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions                                                                   $${n\\geq 3}$$                                                                            n                      ≥                      3}, volume={367}, DOI={<a href=\"https://doi.org/10.1007/s00220-018-3238-1\">10.1007/s00220-018-3238-1</a>}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Souplet, Philippe and Winkler, Michael}, year={2018}, pages={665–681} }","ama":"Souplet P, Winkler M. Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions                                                                   $${n\\geq 3}$$                                                                            n                      ≥                      3. <i>Communications in Mathematical Physics</i>. 2018;367(2):665-681. doi:<a href=\"https://doi.org/10.1007/s00220-018-3238-1\">10.1007/s00220-018-3238-1</a>","ieee":"P. Souplet and M. Winkler, “Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions                                                                   $${n\\geq 3}$$                                                                            n                      ≥                      3,” <i>Communications in Mathematical Physics</i>, vol. 367, no. 2, pp. 665–681, 2018, doi: <a href=\"https://doi.org/10.1007/s00220-018-3238-1\">10.1007/s00220-018-3238-1</a>.","apa":"Souplet, P., &#38; Winkler, M. (2018). Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions                                                                   $${n\\geq 3}$$                                                                            n                      ≥                      3. <i>Communications in Mathematical Physics</i>, <i>367</i>(2), 665–681. <a href=\"https://doi.org/10.1007/s00220-018-3238-1\">https://doi.org/10.1007/s00220-018-3238-1</a>","short":"P. Souplet, M. Winkler, Communications in Mathematical Physics 367 (2018) 665–681.","chicago":"Souplet, Philippe, and Michael Winkler. “Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions                                                                   $${n\\geq 3}$$                                                                            n                      ≥                      3.” <i>Communications in Mathematical Physics</i> 367, no. 2 (2018): 665–81. <a href=\"https://doi.org/10.1007/s00220-018-3238-1\">https://doi.org/10.1007/s00220-018-3238-1</a>."},"issue":"2","publication":"Communications in Mathematical Physics"},{"publisher":"Springer Science and Business Media LLC","_id":"31268","page":"755-822","volume":356,"user_id":"49178","status":"public","external_id":{"arxiv":["1504.06728"]},"citation":{"apa":"Faure, F., &#38; Weich, T. (2017). Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps. <i>Communications in Mathematical Physics</i>, <i>356</i>(3), 755–822. <a href=\"https://doi.org/10.1007/s00220-017-3000-0\">https://doi.org/10.1007/s00220-017-3000-0</a>","ieee":"F. Faure and T. Weich, “Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps,” <i>Communications in Mathematical Physics</i>, vol. 356, no. 3, pp. 755–822, 2017, doi: <a href=\"https://doi.org/10.1007/s00220-017-3000-0\">10.1007/s00220-017-3000-0</a>.","short":"F. Faure, T. Weich, Communications in Mathematical Physics 356 (2017) 755–822.","chicago":"Faure, Frédéric, and Tobias Weich. “Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps.” <i>Communications in Mathematical Physics</i> 356, no. 3 (2017): 755–822. <a href=\"https://doi.org/10.1007/s00220-017-3000-0\">https://doi.org/10.1007/s00220-017-3000-0</a>.","mla":"Faure, Frédéric, and Tobias Weich. “Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps.” <i>Communications in Mathematical Physics</i>, vol. 356, no. 3, Springer Science and Business Media LLC, 2017, pp. 755–822, doi:<a href=\"https://doi.org/10.1007/s00220-017-3000-0\">10.1007/s00220-017-3000-0</a>.","ama":"Faure F, Weich T. Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps. <i>Communications in Mathematical Physics</i>. 2017;356(3):755-822. doi:<a href=\"https://doi.org/10.1007/s00220-017-3000-0\">10.1007/s00220-017-3000-0</a>","bibtex":"@article{Faure_Weich_2017, title={Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps}, volume={356}, DOI={<a href=\"https://doi.org/10.1007/s00220-017-3000-0\">10.1007/s00220-017-3000-0</a>}, number={3}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Faure, Frédéric and Weich, Tobias}, year={2017}, pages={755–822} }"},"language":[{"iso":"eng"}],"doi":"10.1007/s00220-017-3000-0","author":[{"full_name":"Faure, Frédéric","last_name":"Faure","first_name":"Frédéric"},{"full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","first_name":"Tobias","last_name":"Weich","id":"49178"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"year":"2017","title":"Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps","intvolume":"       356","publication_status":"published","date_updated":"2022-05-19T10:14:36Z","date_created":"2022-05-17T12:11:13Z","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"type":"journal_article","publication":"Communications in Mathematical Physics","issue":"3"},{"external_id":{"arxiv":["1403.7419 "]},"citation":{"apa":"Weich, T. (2015). Resonance Chains and Geometric Limits on Schottky Surfaces. <i>Communications in Mathematical Physics</i>, <i>337</i>(2), 727–765. <a href=\"https://doi.org/10.1007/s00220-015-2359-z\">https://doi.org/10.1007/s00220-015-2359-z</a>","ieee":"T. Weich, “Resonance Chains and Geometric Limits on Schottky Surfaces,” <i>Communications in Mathematical Physics</i>, vol. 337, no. 2, pp. 727–765, 2015, doi: <a href=\"https://doi.org/10.1007/s00220-015-2359-z\">10.1007/s00220-015-2359-z</a>.","short":"T. Weich, Communications in Mathematical Physics 337 (2015) 727–765.","chicago":"Weich, Tobias. “Resonance Chains and Geometric Limits on Schottky Surfaces.” <i>Communications in Mathematical Physics</i> 337, no. 2 (2015): 727–65. <a href=\"https://doi.org/10.1007/s00220-015-2359-z\">https://doi.org/10.1007/s00220-015-2359-z</a>.","mla":"Weich, Tobias. “Resonance Chains and Geometric Limits on Schottky Surfaces.” <i>Communications in Mathematical Physics</i>, vol. 337, no. 2, Springer Science and Business Media LLC, 2015, pp. 727–65, doi:<a href=\"https://doi.org/10.1007/s00220-015-2359-z\">10.1007/s00220-015-2359-z</a>.","ama":"Weich T. Resonance Chains and Geometric Limits on Schottky Surfaces. <i>Communications in Mathematical Physics</i>. 2015;337(2):727-765. doi:<a href=\"https://doi.org/10.1007/s00220-015-2359-z\">10.1007/s00220-015-2359-z</a>","bibtex":"@article{Weich_2015, title={Resonance Chains and Geometric Limits on Schottky Surfaces}, volume={337}, DOI={<a href=\"https://doi.org/10.1007/s00220-015-2359-z\">10.1007/s00220-015-2359-z</a>}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Weich, Tobias}, year={2015}, pages={727–765} }"},"volume":337,"user_id":"49178","publisher":"Springer Science and Business Media LLC","_id":"31293","page":"727-765","status":"public","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"date_created":"2022-05-17T12:56:21Z","issue":"2","publication":"Communications in Mathematical Physics","doi":"10.1007/s00220-015-2359-z","language":[{"iso":"eng"}],"intvolume":"       337","date_updated":"2022-05-19T10:16:21Z","publication_status":"published","author":[{"id":"49178","last_name":"Weich","first_name":"Tobias","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"year":"2015","title":"Resonance Chains and Geometric Limits on Schottky Surfaces"},{"date_created":"2024-06-19T08:53:38Z","type":"journal_article","publication":"Communications in Mathematical Physics","issue":"3","citation":{"apa":"Rösler, M. (1998). Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators. <i>Communications in Mathematical Physics</i>, <i>192</i>(3), 519–542. <a href=\"https://doi.org/10.1007/s002200050307\">https://doi.org/10.1007/s002200050307</a>","ieee":"M. Rösler, “Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators,” <i>Communications in Mathematical Physics</i>, vol. 192, no. 3, pp. 519–542, 1998, doi: <a href=\"https://doi.org/10.1007/s002200050307\">10.1007/s002200050307</a>.","chicago":"Rösler, Margit. “Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators.” <i>Communications in Mathematical Physics</i> 192, no. 3 (1998): 519–42. <a href=\"https://doi.org/10.1007/s002200050307\">https://doi.org/10.1007/s002200050307</a>.","short":"M. Rösler, Communications in Mathematical Physics 192 (1998) 519–542.","mla":"Rösler, Margit. “Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators.” <i>Communications in Mathematical Physics</i>, vol. 192, no. 3, Springer Science and Business Media LLC, 1998, pp. 519–42, doi:<a href=\"https://doi.org/10.1007/s002200050307\">10.1007/s002200050307</a>.","ama":"Rösler M. Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators. <i>Communications in Mathematical Physics</i>. 1998;192(3):519-542. doi:<a href=\"https://doi.org/10.1007/s002200050307\">10.1007/s002200050307</a>","bibtex":"@article{Rösler_1998, title={Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators}, volume={192}, DOI={<a href=\"https://doi.org/10.1007/s002200050307\">10.1007/s002200050307</a>}, number={3}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Rösler, Margit}, year={1998}, pages={519–542} }"},"page":"519-542","_id":"54821","publisher":"Springer Science and Business Media LLC","language":[{"iso":"eng"}],"user_id":"82981","doi":"10.1007/s002200050307","volume":192,"title":"Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators","status":"public","year":"1998","author":[{"full_name":"Rösler, Margit","last_name":"Rösler","first_name":"Margit","id":"37390"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"publication_status":"published","date_updated":"2024-07-09T09:09:25Z","intvolume":"       192"}]