--- _id: '2317' abstract: - lang: eng text: 'We present a summary of our recent rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. ' author: - first_name: Rupert full_name: Frank, Rupert L last_name: Frank - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jan full_name: Solovej, Jan P last_name: Solovej citation: ama: 'Frank R, Hainzl C, Seiringer R, Solovej J. Microscopic derivation of the Ginzburg-Landau model. In: World Scientific Publishing; 2012:575-583. doi:10.1142/9789814449243_0060' apa: 'Frank, R., Hainzl, C., Seiringer, R., & Solovej, J. (2012). Microscopic derivation of the Ginzburg-Landau model (pp. 575–583). Presented at the ICMP: International Congress on Mathematical Physics, World Scientific Publishing. https://doi.org/10.1142/9789814449243_0060' chicago: Frank, Rupert, Christian Hainzl, Robert Seiringer, and Jan Solovej. “Microscopic Derivation of the Ginzburg-Landau Model,” 575–83. World Scientific Publishing, 2012. https://doi.org/10.1142/9789814449243_0060. ieee: 'R. Frank, C. Hainzl, R. Seiringer, and J. Solovej, “Microscopic derivation of the Ginzburg-Landau model,” presented at the ICMP: International Congress on Mathematical Physics, 2012, pp. 575–583.' ista: 'Frank R, Hainzl C, Seiringer R, Solovej J. 2012. Microscopic derivation of the Ginzburg-Landau model. ICMP: International Congress on Mathematical Physics, 575–583.' mla: Frank, Rupert, et al. Microscopic Derivation of the Ginzburg-Landau Model. World Scientific Publishing, 2012, pp. 575–83, doi:10.1142/9789814449243_0060. short: R. Frank, C. Hainzl, R. Seiringer, J. Solovej, in:, World Scientific Publishing, 2012, pp. 575–583. conference: name: 'ICMP: International Congress on Mathematical Physics' date_created: 2018-12-11T11:56:57Z date_published: 2012-08-01T00:00:00Z date_updated: 2021-01-12T06:56:44Z day: '01' doi: 10.1142/9789814449243_0060 extern: 1 main_file_link: - open_access: '1' url: http://arxiv.org/abs/1209.1080 month: '08' oa: 1 page: 575 - 583 publication_status: published publisher: World Scientific Publishing publist_id: '4610' quality_controlled: 0 status: public title: Microscopic derivation of the Ginzburg-Landau model type: conference year: '2012' ... --- _id: '2316' abstract: - lang: eng text: 'We summarize our recent results on the ground state energy of multi-polaron systems. In particular, we discuss stability and existence of the thermodynamic limit, and we discuss the absence of binding in the case of large Coulomb repulsion and the corresponding binding-unbinding transition. We also consider the Pekar-Tomasevich approximation to the ground state energy and we study radial symmetry of the ground state density. ' author: - first_name: Rupert full_name: Frank, Rupert L last_name: Frank - first_name: Élliott full_name: Lieb, Élliott H last_name: Lieb - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Lawrence full_name: Thomas, Lawrence E last_name: Thomas citation: ama: 'Frank R, Lieb É, Seiringer R, Thomas L. Ground state properties of multi-polaron systems. In: World Scientific Publishing; 2012:477-485. doi:10.1142/9789814449243_0045' apa: 'Frank, R., Lieb, É., Seiringer, R., & Thomas, L. (2012). Ground state properties of multi-polaron systems (pp. 477–485). Presented at the ICMP: International Congress on Mathematical Physics, World Scientific Publishing. https://doi.org/10.1142/9789814449243_0045' chicago: Frank, Rupert, Élliott Lieb, Robert Seiringer, and Lawrence Thomas. “Ground State Properties of Multi-Polaron Systems,” 477–85. World Scientific Publishing, 2012. https://doi.org/10.1142/9789814449243_0045. ieee: 'R. Frank, É. Lieb, R. Seiringer, and L. Thomas, “Ground state properties of multi-polaron systems,” presented at the ICMP: International Congress on Mathematical Physics, 2012, pp. 477–485.' ista: 'Frank R, Lieb É, Seiringer R, Thomas L. 2012. Ground state properties of multi-polaron systems. ICMP: International Congress on Mathematical Physics, 477–485.' mla: Frank, Rupert, et al. Ground State Properties of Multi-Polaron Systems. World Scientific Publishing, 2012, pp. 477–85, doi:10.1142/9789814449243_0045. short: R. Frank, É. Lieb, R. Seiringer, L. Thomas, in:, World Scientific Publishing, 2012, pp. 477–485. conference: name: 'ICMP: International Congress on Mathematical Physics' date_created: 2018-12-11T11:56:57Z date_published: 2012-08-01T00:00:00Z date_updated: 2021-01-12T06:56:44Z day: '01' doi: 10.1142/9789814449243_0045 extern: 1 main_file_link: - open_access: '1' url: http://arxiv.org/abs/1209.3717 month: '08' oa: 1 page: 477 - 485 publication_status: published publisher: World Scientific Publishing publist_id: '4611' quality_controlled: 0 status: public title: Ground state properties of multi-polaron systems type: conference year: '2012' ... --- _id: '237' abstract: - lang: eng text: The Manin conjecture is established for Châtelet surfaces over Q aris-ing as minimal proper smooth models of the surface Y 2 + Z 2 = f(X) in A 3 Q, where f ∈ Z[X] is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation. acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council" author: - first_name: Régis full_name: de la Bretèche, Régis last_name: De La Bretèche - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Emmanuel full_name: Peyre, Emmanuel last_name: Peyre citation: ama: De La Bretèche R, Browning TD, Peyre E. On Manin’s conjecture for a family of Châtelet surfaces. Annals of Mathematics. 2012;175(1):297-343. doi:10.4007/annals.2012.175.1.8 apa: De La Bretèche, R., Browning, T. D., & Peyre, E. (2012). On Manin’s conjecture for a family of Châtelet surfaces. Annals of Mathematics. Princeton University Press. https://doi.org/10.4007/annals.2012.175.1.8 chicago: De La Bretèche, Régis, Timothy D Browning, and Emmanuel Peyre. “On Manin’s Conjecture for a Family of Châtelet Surfaces.” Annals of Mathematics. Princeton University Press, 2012. https://doi.org/10.4007/annals.2012.175.1.8. ieee: R. De La Bretèche, T. D. Browning, and E. Peyre, “On Manin’s conjecture for a family of Châtelet surfaces,” Annals of Mathematics, vol. 175, no. 1. Princeton University Press, pp. 297–343, 2012. ista: De La Bretèche R, Browning TD, Peyre E. 2012. On Manin’s conjecture for a family of Châtelet surfaces. Annals of Mathematics. 175(1), 297–343. mla: De La Bretèche, Régis, et al. “On Manin’s Conjecture for a Family of Châtelet Surfaces.” Annals of Mathematics, vol. 175, no. 1, Princeton University Press, 2012, pp. 297–343, doi:10.4007/annals.2012.175.1.8. short: R. De La Bretèche, T.D. Browning, E. Peyre, Annals of Mathematics 175 (2012) 297–343. date_created: 2018-12-11T11:45:22Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T06:57:04Z day: '01' doi: 10.4007/annals.2012.175.1.8 extern: 1 intvolume: ' 175' issue: '1' month: '01' page: 297 - 343 publication: Annals of Mathematics publication_status: published publisher: Princeton University Press publist_id: '7667' quality_controlled: 0 status: public title: On Manin's conjecture for a family of Châtelet surfaces type: journal_article volume: 175 year: '2012' ... --- _id: '238' abstract: - lang: eng text: For given positive integers a, b, q we investigate the density of solutions (x, y) ∈ Z2 to congruences ax + by2 ≡ 0 mod q. acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council" author: - first_name: Stephan full_name: Baier, Stephan last_name: Baier - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 citation: ama: Baier S, Browning TD. Inhomogeneous quadratic congruences. Functiones et Approximatio, Commentarii Mathematici. 2012;47(2):267-286. doi:10.7169/facm/2012.47.2.9 apa: Baier, S., & Browning, T. D. (2012). Inhomogeneous quadratic congruences. Functiones et Approximatio, Commentarii Mathematici. Adam Mickiewicz University Press. https://doi.org/10.7169/facm/2012.47.2.9 chicago: Baier, Stephan, and Timothy D Browning. “Inhomogeneous Quadratic Congruences.” Functiones et Approximatio, Commentarii Mathematici. Adam Mickiewicz University Press, 2012. https://doi.org/10.7169/facm/2012.47.2.9. ieee: S. Baier and T. D. Browning, “Inhomogeneous quadratic congruences,” Functiones et Approximatio, Commentarii Mathematici, vol. 47, no. 2. Adam Mickiewicz University Press, pp. 267–286, 2012. ista: Baier S, Browning TD. 2012. Inhomogeneous quadratic congruences. Functiones et Approximatio, Commentarii Mathematici. 47(2), 267–286. mla: Baier, Stephan, and Timothy D. Browning. “Inhomogeneous Quadratic Congruences.” Functiones et Approximatio, Commentarii Mathematici, vol. 47, no. 2, Adam Mickiewicz University Press, 2012, pp. 267–86, doi:10.7169/facm/2012.47.2.9. short: S. Baier, T.D. Browning, Functiones et Approximatio, Commentarii Mathematici 47 (2012) 267–286. date_created: 2018-12-11T11:45:22Z date_published: 2012-12-20T00:00:00Z date_updated: 2021-01-12T06:57:08Z day: '20' doi: 10.7169/facm/2012.47.2.9 extern: 1 intvolume: ' 47' issue: '2' month: '12' page: 267 - 286 publication: Functiones et Approximatio, Commentarii Mathematici publication_status: published publisher: Adam Mickiewicz University Press publist_id: '7666' quality_controlled: 0 status: public title: Inhomogeneous quadratic congruences type: journal_article volume: 47 year: '2012' ... --- _id: '2399' abstract: - lang: eng text: | Bose–Einstein condensation (BEC) in cold atomic gases was first achieved experimentally in 1995 [1, 6]. After initial failed attempts with spin-polarized atomic hydrogen, the first successful demonstrations of this phenomenon used gases of rubidium and sodium atoms, respectively. Since then there has been a surge of activity in this field, with ingenious experiments putting forth more and more astonishing results about the behavior of matter at very cold temperatures. alternative_title: - Lecture Notes in Mathematics author: - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Seiringer R. Cold quantum gases and bose einstein condensation. In: Rivasseau V, Seiringer R, Solovej J, Spencer T, eds. Quantum Many Body Systems. Vol 2051. Springer; 2012:55-92. doi:10.1007/978-3-642-29511-9_2' apa: Seiringer, R. (2012). Cold quantum gases and bose einstein condensation. In V. Rivasseau, R. Seiringer, J. Solovej, & T. Spencer (Eds.), Quantum Many Body Systems (Vol. 2051, pp. 55–92). Springer. https://doi.org/10.1007/978-3-642-29511-9_2 chicago: Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.” In Quantum Many Body Systems, edited by Vincent Rivasseau, Robert Seiringer, Jan Solovej, and Thomas Spencer, 2051:55–92. Springer, 2012. https://doi.org/10.1007/978-3-642-29511-9_2. ieee: R. Seiringer, “Cold quantum gases and bose einstein condensation,” in Quantum Many Body Systems, vol. 2051, V. Rivasseau, R. Seiringer, J. Solovej, and T. Spencer, Eds. Springer, 2012, pp. 55–92. ista: 'Seiringer R. 2012.Cold quantum gases and bose einstein condensation. In: Quantum Many Body Systems. Lecture Notes in Mathematics, vol. 2051, 55–92.' mla: Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.” Quantum Many Body Systems, edited by Vincent Rivasseau et al., vol. 2051, Springer, 2012, pp. 55–92, doi:10.1007/978-3-642-29511-9_2. short: R. Seiringer, in:, V. Rivasseau, R. Seiringer, J. Solovej, T. Spencer (Eds.), Quantum Many Body Systems, Springer, 2012, pp. 55–92. date_created: 2018-12-11T11:57:26Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T06:57:14Z day: '01' doi: 10.1007/978-3-642-29511-9_2 editor: - first_name: Vincent full_name: Rivasseau, Vincent last_name: Rivasseau - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jan full_name: Solovej, Jan P last_name: Solovej - first_name: Thomas full_name: Spencer, Thomas last_name: Spencer extern: 1 intvolume: ' 2051' month: '01' page: 55 - 92 publication: Quantum Many Body Systems publication_status: published publisher: Springer publist_id: '4526' quality_controlled: 0 status: public title: Cold quantum gases and bose einstein condensation type: book_chapter volume: 2051 year: '2012' ... --- _id: '2394' abstract: - lang: eng text: We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For cosh (δ μ/T) ≤ 2, with T the temperature and δμ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in [Frank, R. L., Hainzl, C., Naboko, S., and Seiringer, R., J., Geom. Anal.17, 559-567 (2007)10.1007/BF02937429; Hainzl, C., Hamza, E., Seiringer, R., and Solovej, J. P., Commun., Math. Phys.281, 349-367 (2008)10.1007/s00220-008-0489-2; and Hainzl, C. and Seiringer, R., Phys. Rev. B77, 184517-110 435 (2008)]10.1103/PhysRevB.77.184517. For cosh (δ μ/T) > 2 the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit. author: - first_name: Abraham full_name: Freiji, Abraham last_name: Freiji - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Freiji A, Hainzl C, Seiringer R. The gap equation for spin-polarized fermions. Journal of Mathematical Physics. 2012;53(1). doi:10.1063/1.3670747 apa: Freiji, A., Hainzl, C., & Seiringer, R. (2012). The gap equation for spin-polarized fermions. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.3670747 chicago: Freiji, Abraham, Christian Hainzl, and Robert Seiringer. “The Gap Equation for Spin-Polarized Fermions.” Journal of Mathematical Physics. American Institute of Physics, 2012. https://doi.org/10.1063/1.3670747. ieee: A. Freiji, C. Hainzl, and R. Seiringer, “The gap equation for spin-polarized fermions,” Journal of Mathematical Physics, vol. 53, no. 1. American Institute of Physics, 2012. ista: Freiji A, Hainzl C, Seiringer R. 2012. The gap equation for spin-polarized fermions. Journal of Mathematical Physics. 53(1). mla: Freiji, Abraham, et al. “The Gap Equation for Spin-Polarized Fermions.” Journal of Mathematical Physics, vol. 53, no. 1, American Institute of Physics, 2012, doi:10.1063/1.3670747. short: A. Freiji, C. Hainzl, R. Seiringer, Journal of Mathematical Physics 53 (2012). date_created: 2018-12-11T11:57:25Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T06:57:13Z day: '01' doi: 10.1063/1.3670747 extern: 1 intvolume: ' 53' issue: '1' month: '01' publication: Journal of Mathematical Physics publication_status: published publisher: American Institute of Physics publist_id: '4532' quality_controlled: 0 status: public title: The gap equation for spin-polarized fermions type: journal_article volume: 53 year: '2012' ... --- _id: '2395' abstract: - lang: eng text: 'We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. ' author: - first_name: Rupert full_name: Frank, Rupert L last_name: Frank - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jan full_name: Solovej, Jan P last_name: Solovej citation: ama: Frank R, Hainzl C, Seiringer R, Solovej J. Microscopic derivation of Ginzburg-Landau theory. Journal of the American Mathematical Society. 2012;25(3):667-713. doi:10.1090/S0894-0347-2012-00735-8 apa: Frank, R., Hainzl, C., Seiringer, R., & Solovej, J. (2012). Microscopic derivation of Ginzburg-Landau theory. Journal of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/S0894-0347-2012-00735-8 chicago: Frank, Rupert, Christian Hainzl, Robert Seiringer, and Jan Solovej. “Microscopic Derivation of Ginzburg-Landau Theory.” Journal of the American Mathematical Society. American Mathematical Society, 2012. https://doi.org/10.1090/S0894-0347-2012-00735-8. ieee: R. Frank, C. Hainzl, R. Seiringer, and J. Solovej, “Microscopic derivation of Ginzburg-Landau theory,” Journal of the American Mathematical Society, vol. 25, no. 3. American Mathematical Society, pp. 667–713, 2012. ista: Frank R, Hainzl C, Seiringer R, Solovej J. 2012. Microscopic derivation of Ginzburg-Landau theory. Journal of the American Mathematical Society. 25(3), 667–713. mla: Frank, Rupert, et al. “Microscopic Derivation of Ginzburg-Landau Theory.” Journal of the American Mathematical Society, vol. 25, no. 3, American Mathematical Society, 2012, pp. 667–713, doi:10.1090/S0894-0347-2012-00735-8. short: R. Frank, C. Hainzl, R. Seiringer, J. Solovej, Journal of the American Mathematical Society 25 (2012) 667–713. date_created: 2018-12-11T11:57:25Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T06:57:13Z day: '01' doi: 10.1090/S0894-0347-2012-00735-8 extern: 1 intvolume: ' 25' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1102.4001 month: '01' oa: 1 page: 667 - 713 publication: Journal of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '4531' quality_controlled: 0 status: public title: Microscopic derivation of Ginzburg-Landau theory type: journal_article volume: 25 year: '2012' ... --- _id: '2396' abstract: - lang: eng text: A positive temperature analogue of the scattering length of a potential V can be defined via integrating the difference of the heat kernels of -Δ and, with Δ the Laplacian. An upper bound on this quantity is a crucial input in the derivation of a bound on the critical temperature of a dilute Bose gas (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009). In (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009), a bound was given in the case of finite range potentials and sufficiently low temperature. In this paper, we improve the bound and extend it to potentials of infinite range. author: - first_name: Benjamin full_name: Landon, Benjamin last_name: Landon - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Landon B, Seiringer R. The scattering length at positive temperature. Letters in Mathematical Physics. 2012;100(3):237-243. doi:10.1007/s11005-012-0566-5 apa: Landon, B., & Seiringer, R. (2012). The scattering length at positive temperature. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-012-0566-5 chicago: Landon, Benjamin, and Robert Seiringer. “The Scattering Length at Positive Temperature.” Letters in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s11005-012-0566-5. ieee: B. Landon and R. Seiringer, “The scattering length at positive temperature,” Letters in Mathematical Physics, vol. 100, no. 3. Springer, pp. 237–243, 2012. ista: Landon B, Seiringer R. 2012. The scattering length at positive temperature. Letters in Mathematical Physics. 100(3), 237–243. mla: Landon, Benjamin, and Robert Seiringer. “The Scattering Length at Positive Temperature.” Letters in Mathematical Physics, vol. 100, no. 3, Springer, 2012, pp. 237–43, doi:10.1007/s11005-012-0566-5. short: B. Landon, R. Seiringer, Letters in Mathematical Physics 100 (2012) 237–243. date_created: 2018-12-11T11:57:25Z date_published: 2012-06-01T00:00:00Z date_updated: 2021-01-12T06:57:13Z day: '01' doi: 10.1007/s11005-012-0566-5 extern: 1 intvolume: ' 100' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1111.1683 month: '06' oa: 1 page: 237 - 243 publication: Letters in Mathematical Physics publication_status: published publisher: Springer publist_id: '4529' quality_controlled: 0 status: public title: The scattering length at positive temperature type: journal_article volume: 100 year: '2012' ... --- _id: '2398' abstract: - lang: eng text: We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time. author: - first_name: Vojkan full_name: Jakšić, Vojkan last_name: Jakšić - first_name: Yoshiko full_name: Ogata, Yoshiko last_name: Ogata - first_name: Claude full_name: Pillet, Claude A last_name: Pillet - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Jakšić V, Ogata Y, Pillet C, Seiringer R. Quantum hypothesis testing and non-equilibrium statistical mechanics. Reviews in Mathematical Physics. 2012;24(6). doi:10.1142/S0129055X12300026 apa: Jakšić, V., Ogata, Y., Pillet, C., & Seiringer, R. (2012). Quantum hypothesis testing and non-equilibrium statistical mechanics. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X12300026 chicago: Jakšić, Vojkan, Yoshiko Ogata, Claude Pillet, and Robert Seiringer. “Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics.” Reviews in Mathematical Physics. World Scientific Publishing, 2012. https://doi.org/10.1142/S0129055X12300026. ieee: V. Jakšić, Y. Ogata, C. Pillet, and R. Seiringer, “Quantum hypothesis testing and non-equilibrium statistical mechanics,” Reviews in Mathematical Physics, vol. 24, no. 6. World Scientific Publishing, 2012. ista: Jakšić V, Ogata Y, Pillet C, Seiringer R. 2012. Quantum hypothesis testing and non-equilibrium statistical mechanics. Reviews in Mathematical Physics. 24(6). mla: Jakšić, Vojkan, et al. “Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics.” Reviews in Mathematical Physics, vol. 24, no. 6, World Scientific Publishing, 2012, doi:10.1142/S0129055X12300026. short: V. Jakšić, Y. Ogata, C. Pillet, R. Seiringer, Reviews in Mathematical Physics 24 (2012). date_created: 2018-12-11T11:57:26Z date_published: 2012-07-01T00:00:00Z date_updated: 2020-07-14T12:45:40Z day: '01' doi: 10.1142/S0129055X12300026 extern: 1 intvolume: ' 24' issue: '6' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1109.3804 month: '07' oa: 1 publication: Reviews in Mathematical Physics publication_status: published publisher: World Scientific Publishing publist_id: '4528' quality_controlled: 0 status: public title: Quantum hypothesis testing and non-equilibrium statistical mechanics type: review volume: 24 year: '2012' ... --- _id: '2397' abstract: - lang: eng text: We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs. author: - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Hainzl C, Seiringer R. Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. Letters in Mathematical Physics. 2012;100(2):119-138. doi:10.1007/s11005-011-0535-4 apa: Hainzl, C., & Seiringer, R. (2012). Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-011-0535-4 chicago: Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs.” Letters in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s11005-011-0535-4. ieee: C. Hainzl and R. Seiringer, “Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs,” Letters in Mathematical Physics, vol. 100, no. 2. Springer, pp. 119–138, 2012. ista: Hainzl C, Seiringer R. 2012. Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. Letters in Mathematical Physics. 100(2), 119–138. mla: Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs.” Letters in Mathematical Physics, vol. 100, no. 2, Springer, 2012, pp. 119–38, doi:10.1007/s11005-011-0535-4. short: C. Hainzl, R. Seiringer, Letters in Mathematical Physics 100 (2012) 119–138. date_created: 2018-12-11T11:57:25Z date_published: 2012-05-01T00:00:00Z date_updated: 2021-01-12T06:57:14Z day: '01' doi: 10.1007/s11005-011-0535-4 extern: 1 intvolume: ' 100' issue: '2' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1105.1100 month: '05' oa: 1 page: 119 - 138 publication: Letters in Mathematical Physics publication_status: published publisher: Springer publist_id: '4530' quality_controlled: 0 status: public title: Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs type: journal_article volume: 100 year: '2012' ... --- _id: '240' abstract: - lang: eng text: We investigate the frequency of positive squareful numbers x, y, z≤B for which x+y=z and present a conjecture concerning its asymptotic behavior. acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council" author: - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: K Van full_name: Valckenborgh, K Van last_name: Valckenborgh citation: ama: Browning TD, Valckenborgh KV. Sums of three squareful numbers. Experimental Mathematics. 2012;21(2):204-211. doi:10.1080/10586458.2011.605733 apa: Browning, T. D., & Valckenborgh, K. V. (2012). Sums of three squareful numbers. Experimental Mathematics. Taylor & Francis. https://doi.org/10.1080/10586458.2011.605733 chicago: Browning, Timothy D, and K Van Valckenborgh. “Sums of Three Squareful Numbers.” Experimental Mathematics. Taylor & Francis, 2012. https://doi.org/10.1080/10586458.2011.605733. ieee: T. D. Browning and K. V. Valckenborgh, “Sums of three squareful numbers,” Experimental Mathematics, vol. 21, no. 2. Taylor & Francis, pp. 204–211, 2012. ista: Browning TD, Valckenborgh KV. 2012. Sums of three squareful numbers. Experimental Mathematics. 21(2), 204–211. mla: Browning, Timothy D., and K. Van Valckenborgh. “Sums of Three Squareful Numbers.” Experimental Mathematics, vol. 21, no. 2, Taylor & Francis, 2012, pp. 204–11, doi:10.1080/10586458.2011.605733. short: T.D. Browning, K.V. Valckenborgh, Experimental Mathematics 21 (2012) 204–211. date_created: 2018-12-11T11:45:23Z date_published: 2012-05-23T00:00:00Z date_updated: 2021-01-12T06:57:15Z day: '23' doi: 10.1080/10586458.2011.605733 extern: 1 intvolume: ' 21' issue: '2' month: '05' page: 204 - 211 publication: Experimental Mathematics publication_status: published publisher: Taylor & Francis publist_id: '7664' quality_controlled: 0 status: public title: Sums of three squareful numbers type: journal_article volume: 21 year: '2012' ... --- _id: '2400' abstract: - lang: eng text: If the polaron coupling constant α is large enough, bipolarons or multi-polarons will form. When passing through the critical α c from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explode? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at α c. Similarly, we show that the same phenomenon occurs for atoms, e. g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger equation, and are very general. They use the fact that the Coulomb repulsion decays like 1/r, while 'uncertainty principle' localization energies decay more rapidly, as 1/r 2. author: - first_name: Rupert full_name: Frank, Rupert L last_name: Frank - first_name: Élliott full_name: Lieb, Élliott H last_name: Lieb - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Frank R, Lieb É, Seiringer R. Binding of polarons and atoms at threshold. Communications in Mathematical Physics. 2012;313(2):405-424. doi:10.1007/s00220-012-1436-9 apa: Frank, R., Lieb, É., & Seiringer, R. (2012). Binding of polarons and atoms at threshold. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-012-1436-9 chicago: Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Binding of Polarons and Atoms at Threshold.” Communications in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-012-1436-9. ieee: R. Frank, É. Lieb, and R. Seiringer, “Binding of polarons and atoms at threshold,” Communications in Mathematical Physics, vol. 313, no. 2. Springer, pp. 405–424, 2012. ista: Frank R, Lieb É, Seiringer R. 2012. Binding of polarons and atoms at threshold. Communications in Mathematical Physics. 313(2), 405–424. mla: Frank, Rupert, et al. “Binding of Polarons and Atoms at Threshold.” Communications in Mathematical Physics, vol. 313, no. 2, Springer, 2012, pp. 405–24, doi:10.1007/s00220-012-1436-9. short: R. Frank, É. Lieb, R. Seiringer, Communications in Mathematical Physics 313 (2012) 405–424. date_created: 2018-12-11T11:57:27Z date_published: 2012-07-01T00:00:00Z date_updated: 2021-01-12T06:57:15Z day: '01' doi: 10.1007/s00220-012-1436-9 extern: 1 intvolume: ' 313' issue: '2' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1106.0729 month: '07' oa: 1 page: 405 - 424 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '4527' quality_controlled: 0 status: public title: Binding of polarons and atoms at threshold type: journal_article volume: 313 year: '2012' ... --- _id: '2403' abstract: - lang: eng text: We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose-Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval. author: - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jakob full_name: Yngvason, Jakob last_name: Yngvason - first_name: Valentin full_name: Zagrebnov, Valentin A last_name: Zagrebnov citation: ama: Seiringer R, Yngvason J, Zagrebnov V. Disordered Bose-Einstein condensates with interaction in one dimension. Journal of Statistical Mechanics Theory and Experiment. 2012;2012(11). doi:10.1088/1742-5468/2012/11/P11007 apa: Seiringer, R., Yngvason, J., & Zagrebnov, V. (2012). Disordered Bose-Einstein condensates with interaction in one dimension. Journal of Statistical Mechanics Theory and Experiment. IOP Publishing Ltd. https://doi.org/10.1088/1742-5468/2012/11/P11007 chicago: Seiringer, Robert, Jakob Yngvason, and Valentin Zagrebnov. “Disordered Bose-Einstein Condensates with Interaction in One Dimension.” Journal of Statistical Mechanics Theory and Experiment. IOP Publishing Ltd., 2012. https://doi.org/10.1088/1742-5468/2012/11/P11007. ieee: R. Seiringer, J. Yngvason, and V. Zagrebnov, “Disordered Bose-Einstein condensates with interaction in one dimension,” Journal of Statistical Mechanics Theory and Experiment, vol. 2012, no. 11. IOP Publishing Ltd., 2012. ista: Seiringer R, Yngvason J, Zagrebnov V. 2012. Disordered Bose-Einstein condensates with interaction in one dimension. Journal of Statistical Mechanics Theory and Experiment. 2012(11). mla: Seiringer, Robert, et al. “Disordered Bose-Einstein Condensates with Interaction in One Dimension.” Journal of Statistical Mechanics Theory and Experiment, vol. 2012, no. 11, IOP Publishing Ltd., 2012, doi:10.1088/1742-5468/2012/11/P11007. short: R. Seiringer, J. Yngvason, V. Zagrebnov, Journal of Statistical Mechanics Theory and Experiment 2012 (2012). date_created: 2018-12-11T11:57:28Z date_published: 2012-11-01T00:00:00Z date_updated: 2021-01-12T06:57:16Z day: '01' doi: 10.1088/1742-5468/2012/11/P11007 extern: 1 intvolume: ' 2012' issue: '11' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1207.7054 month: '11' oa: 1 publication: Journal of Statistical Mechanics Theory and Experiment publication_status: published publisher: IOP Publishing Ltd. publist_id: '4523' quality_controlled: 0 status: public title: Disordered Bose-Einstein condensates with interaction in one dimension type: journal_article volume: 2012 year: '2012' ... --- _id: '2402' abstract: - lang: eng text: We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from below by a constant times the integral of the particle density to the power. author: - first_name: Rupert full_name: Frank, Rupert L last_name: Frank - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Frank R, Seiringer R. Lieb-Thirring inequality for a model of particles with point interactions. Journal of Mathematical Physics. 2012;53(9). doi:10.1063/1.3697416 apa: Frank, R., & Seiringer, R. (2012). Lieb-Thirring inequality for a model of particles with point interactions. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.3697416 chicago: Frank, Rupert, and Robert Seiringer. “Lieb-Thirring Inequality for a Model of Particles with Point Interactions.” Journal of Mathematical Physics. American Institute of Physics, 2012. https://doi.org/10.1063/1.3697416. ieee: R. Frank and R. Seiringer, “Lieb-Thirring inequality for a model of particles with point interactions,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012. ista: Frank R, Seiringer R. 2012. Lieb-Thirring inequality for a model of particles with point interactions. Journal of Mathematical Physics. 53(9). mla: Frank, Rupert, and Robert Seiringer. “Lieb-Thirring Inequality for a Model of Particles with Point Interactions.” Journal of Mathematical Physics, vol. 53, no. 9, American Institute of Physics, 2012, doi:10.1063/1.3697416. short: R. Frank, R. Seiringer, Journal of Mathematical Physics 53 (2012). date_created: 2018-12-11T11:57:27Z date_published: 2012-09-28T00:00:00Z date_updated: 2021-01-12T06:57:16Z day: '28' doi: 10.1063/1.3697416 extern: 1 intvolume: ' 53' issue: '9' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1112.5617 month: '09' oa: 1 publication: Journal of Mathematical Physics publication_status: published publisher: American Institute of Physics publist_id: '4524' quality_controlled: 0 status: public title: Lieb-Thirring inequality for a model of particles with point interactions type: journal_article volume: 53 year: '2012' ... --- _id: '2401' abstract: - lang: eng text: We find further implications of the BMV conjecture, which states that for hermitian matrices B≥0 and A, the function λ {mapping} Tr exp(A - λB) is the Laplace transform of a positive measure supported on [0,∞]. author: - first_name: Élliott full_name: Lieb, Élliott H last_name: Lieb - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Lieb É, Seiringer R. Further implications of the Bessis-Moussa-Villani conjecture. Journal of Statistical Physics. 2012;149(1):86-91. doi:10.1007/s10955-012-0585-8 apa: Lieb, É., & Seiringer, R. (2012). Further implications of the Bessis-Moussa-Villani conjecture. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-012-0585-8 chicago: Lieb, Élliott, and Robert Seiringer. “Further Implications of the Bessis-Moussa-Villani Conjecture.” Journal of Statistical Physics. Springer, 2012. https://doi.org/10.1007/s10955-012-0585-8. ieee: É. Lieb and R. Seiringer, “Further implications of the Bessis-Moussa-Villani conjecture,” Journal of Statistical Physics, vol. 149, no. 1. Springer, pp. 86–91, 2012. ista: Lieb É, Seiringer R. 2012. Further implications of the Bessis-Moussa-Villani conjecture. Journal of Statistical Physics. 149(1), 86–91. mla: Lieb, Élliott, and Robert Seiringer. “Further Implications of the Bessis-Moussa-Villani Conjecture.” Journal of Statistical Physics, vol. 149, no. 1, Springer, 2012, pp. 86–91, doi:10.1007/s10955-012-0585-8. short: É. Lieb, R. Seiringer, Journal of Statistical Physics 149 (2012) 86–91. date_created: 2018-12-11T11:57:27Z date_published: 2012-10-01T00:00:00Z date_updated: 2021-01-12T06:57:16Z day: '01' doi: 10.1007/s10955-012-0585-8 extern: 1 intvolume: ' 149' issue: '1' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1206.0460 month: '10' oa: 1 page: 86 - 91 publication: Journal of Statistical Physics publication_status: published publisher: Springer publist_id: '4525' quality_controlled: 0 status: public title: Further implications of the Bessis-Moussa-Villani conjecture type: journal_article volume: 149 year: '2012' ... --- _id: '2411' abstract: - lang: eng text: The kingdom of fungi provides model organisms for biotechnology, cell biology, genetics, and life sciences in general. Only when their phylogenetic relationships are stably resolved, can individual results from fungal research be integrated into a holistic picture of biology. However, and despite recent progress, many deep relationships within the fungi remain unclear. Here, we present the first phylogenomic study of an entire eukaryotic kingdom that uses a consistency criterion to strengthen phylogenetic conclusions. We reason that branches (splits) recovered with independent data and different tree reconstruction methods are likely to reflect true evolutionary relationships. Two complementary phylogenomic data sets based on 99 fungal genomes and 109 fungal expressed sequence tag (EST) sets analyzed with four different tree reconstruction methods shed light from different angles on the fungal tree of life. Eleven additional data sets address specifically the phylogenetic position of Blastocladiomycota, Ustilaginomycotina, and Dothideomycetes, respectively. The combined evidence from the resulting trees supports the deep-level stability of the fungal groups toward a comprehensive natural system of the fungi. In addition, our analysis reveals methodologically interesting aspects. Enrichment for EST encoded data-a common practice in phylogenomic analyses-introduces a strong bias toward slowly evolving and functionally correlated genes. Consequently, the generalization of phylogenomic data sets as collections of randomly selected genes cannot be taken for granted. A thorough characterization of the data to assess possible influences on the tree reconstruction should therefore become a standard in phylogenomic analyses. author: - first_name: Ingo full_name: Ebersberger, Ingo last_name: Ebersberger - first_name: Ricardo full_name: De Matos Simoes, Ricardo last_name: De Matos Simoes - first_name: Anne full_name: Kupczok, Anne id: 2BB22BC2-F248-11E8-B48F-1D18A9856A87 last_name: Kupczok - first_name: Matthias full_name: Gube, Matthias last_name: Gube - first_name: Erika full_name: Kothe, Erika last_name: Kothe - first_name: Kerstin full_name: Voigt, Kerstin last_name: Voigt - first_name: Arndt full_name: Von Haeseler, Arndt last_name: Von Haeseler citation: ama: Ebersberger I, De Matos Simoes R, Kupczok A, et al. A consistent phylogenetic backbone for the fungi. Molecular Biology and Evolution. 2012;29(5):1319-1334. doi:10.1093/molbev/msr285 apa: Ebersberger, I., De Matos Simoes, R., Kupczok, A., Gube, M., Kothe, E., Voigt, K., & Von Haeseler, A. (2012). A consistent phylogenetic backbone for the fungi. Molecular Biology and Evolution. Oxford University Press. https://doi.org/10.1093/molbev/msr285 chicago: Ebersberger, Ingo, Ricardo De Matos Simoes, Anne Kupczok, Matthias Gube, Erika Kothe, Kerstin Voigt, and Arndt Von Haeseler. “A Consistent Phylogenetic Backbone for the Fungi.” Molecular Biology and Evolution. Oxford University Press, 2012. https://doi.org/10.1093/molbev/msr285. ieee: I. Ebersberger et al., “A consistent phylogenetic backbone for the fungi,” Molecular Biology and Evolution, vol. 29, no. 5. Oxford University Press, pp. 1319–1334, 2012. ista: Ebersberger I, De Matos Simoes R, Kupczok A, Gube M, Kothe E, Voigt K, Von Haeseler A. 2012. A consistent phylogenetic backbone for the fungi. Molecular Biology and Evolution. 29(5), 1319–1334. mla: Ebersberger, Ingo, et al. “A Consistent Phylogenetic Backbone for the Fungi.” Molecular Biology and Evolution, vol. 29, no. 5, Oxford University Press, 2012, pp. 1319–34, doi:10.1093/molbev/msr285. short: I. Ebersberger, R. De Matos Simoes, A. Kupczok, M. Gube, E. Kothe, K. Voigt, A. Von Haeseler, Molecular Biology and Evolution 29 (2012) 1319–1334. date_created: 2018-12-11T11:57:30Z date_published: 2012-05-01T00:00:00Z date_updated: 2021-01-12T06:57:19Z day: '01' ddc: - '570' - '576' department: - _id: JoBo doi: 10.1093/molbev/msr285 file: - access_level: open_access checksum: d565dcac27d1736c0c378ea6fcf22d69 content_type: application/pdf creator: system date_created: 2018-12-12T10:13:30Z date_updated: 2020-07-14T12:45:40Z file_id: '5013' file_name: IST-2015-384-v1+1_Mol_Biol_Evol-2012-Ebersberger-1319-34.pdf file_size: 754922 relation: main_file file_date_updated: 2020-07-14T12:45:40Z has_accepted_license: '1' intvolume: ' 29' issue: '5' language: - iso: eng license: https://creativecommons.org/licenses/by-nc/4.0/ month: '05' oa: 1 oa_version: Published Version page: 1319 - 1334 publication: Molecular Biology and Evolution publication_status: published publisher: Oxford University Press publist_id: '4515' pubrep_id: '384' quality_controlled: '1' scopus_import: 1 status: public title: A consistent phylogenetic backbone for the fungi tmp: image: /images/cc_by_nc.png legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) short: CC BY-NC (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 29 year: '2012' ... --- _id: '241' abstract: - lang: eng text: The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Châtelet surfaces over ℚ. author: - first_name: Régis full_name: de la Bretèche, Régis last_name: De La Bretèche - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 citation: ama: De La Bretèche R, Browning TD. Binary forms as sums of two squares and Châtelet surfaces. Israel Journal of Mathematics. 2012;191(2):973-1012. doi:10.1007/s11856-012-0019-y apa: De La Bretèche, R., & Browning, T. D. (2012). Binary forms as sums of two squares and Châtelet surfaces. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-012-0019-y chicago: De La Bretèche, Régis, and Timothy D Browning. “Binary Forms as Sums of Two Squares and Châtelet Surfaces.” Israel Journal of Mathematics. Springer, 2012. https://doi.org/10.1007/s11856-012-0019-y. ieee: R. De La Bretèche and T. D. Browning, “Binary forms as sums of two squares and Châtelet surfaces,” Israel Journal of Mathematics, vol. 191, no. 2. Springer, pp. 973–1012, 2012. ista: De La Bretèche R, Browning TD. 2012. Binary forms as sums of two squares and Châtelet surfaces. Israel Journal of Mathematics. 191(2), 973–1012. mla: De La Bretèche, Régis, and Timothy D. Browning. “Binary Forms as Sums of Two Squares and Châtelet Surfaces.” Israel Journal of Mathematics, vol. 191, no. 2, Springer, 2012, pp. 973–1012, doi:10.1007/s11856-012-0019-y. short: R. De La Bretèche, T.D. Browning, Israel Journal of Mathematics 191 (2012) 973–1012. date_created: 2018-12-11T11:45:23Z date_published: 2012-02-28T00:00:00Z date_updated: 2021-01-12T06:57:19Z day: '28' doi: 10.1007/s11856-012-0019-y extern: 1 intvolume: ' 191' issue: '2' month: '02' page: 973 - 1012 publication: Israel Journal of Mathematics publication_status: published publisher: Springer publist_id: '7663' quality_controlled: 0 status: public title: Binary forms as sums of two squares and Châtelet surfaces type: journal_article volume: 191 year: '2012' ... --- _id: '242' abstract: - lang: eng text: We investigate the first and second moments of shifted convolutions of the generalized divisor function d 3(n). acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council" author: - first_name: Stephan full_name: Baier, Stephan last_name: Baier - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Gihan full_name: Marasingha, Gihan last_name: Marasingha - first_name: Liangyi full_name: Zhao, Liangyi last_name: Zhao citation: ama: Baier S, Browning TD, Marasingha G, Zhao L. Averages of shifted convolutions of d3 (n). Proceedings of the Edinburgh Mathematical Society. 2012;55(3):551-576. doi:10.1017/S001309151100037X apa: Baier, S., Browning, T. D., Marasingha, G., & Zhao, L. (2012). Averages of shifted convolutions of d3 (n). Proceedings of the Edinburgh Mathematical Society. Cambridge University Press. https://doi.org/10.1017/S001309151100037X chicago: Baier, Stephan, Timothy D Browning, Gihan Marasingha, and Liangyi Zhao. “Averages of Shifted Convolutions of D3 (N).” Proceedings of the Edinburgh Mathematical Society. Cambridge University Press, 2012. https://doi.org/10.1017/S001309151100037X. ieee: S. Baier, T. D. Browning, G. Marasingha, and L. Zhao, “Averages of shifted convolutions of d3 (n),” Proceedings of the Edinburgh Mathematical Society, vol. 55, no. 3. Cambridge University Press, pp. 551–576, 2012. ista: Baier S, Browning TD, Marasingha G, Zhao L. 2012. Averages of shifted convolutions of d3 (n). Proceedings of the Edinburgh Mathematical Society. 55(3), 551–576. mla: Baier, Stephan, et al. “Averages of Shifted Convolutions of D3 (N).” Proceedings of the Edinburgh Mathematical Society, vol. 55, no. 3, Cambridge University Press, 2012, pp. 551–76, doi:10.1017/S001309151100037X. short: S. Baier, T.D. Browning, G. Marasingha, L. Zhao, Proceedings of the Edinburgh Mathematical Society 55 (2012) 551–576. date_created: 2018-12-11T11:45:23Z date_published: 2012-10-01T00:00:00Z date_updated: 2021-01-12T06:57:23Z day: '01' doi: 10.1017/S001309151100037X extern: 1 intvolume: ' 55' issue: '3' main_file_link: - open_access: '1' url: https://arxiv.org/abs/1101.5464 month: '10' oa: 1 page: 551 - 576 publication: Proceedings of the Edinburgh Mathematical Society publication_status: published publisher: Cambridge University Press publist_id: '7662' quality_controlled: 0 status: public title: Averages of shifted convolutions of d3 (n) type: journal_article volume: 55 year: '2012' ... --- _id: '243' abstract: - lang: eng text: Let P(t) ∈ ℚ[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of ℚ containing the roots of P(t). Let N K/ℚ(X) be a full norm form for the extension K/ℚ. We show that the variety P(t) =N K/ℚ(X)≠ 0 satisfies the Hasse principle and weak approximation. The proof uses analytic methods. author: - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Roger full_name: Heath-Brown, Roger last_name: Heath Brown citation: ama: Browning TD, Heath Brown R. Quadratic polynomials represented by norm forms. Geometric and Functional Analysis. 2012;22(5):1124-1190. doi:10.1007/s00039-012-0168-5 apa: Browning, T. D., & Heath Brown, R. (2012). Quadratic polynomials represented by norm forms. Geometric and Functional Analysis. Springer Basel. https://doi.org/10.1007/s00039-012-0168-5 chicago: Browning, Timothy D, and Roger Heath Brown. “Quadratic Polynomials Represented by Norm Forms.” Geometric and Functional Analysis. Springer Basel, 2012. https://doi.org/10.1007/s00039-012-0168-5. ieee: T. D. Browning and R. Heath Brown, “Quadratic polynomials represented by norm forms,” Geometric and Functional Analysis, vol. 22, no. 5. Springer Basel, pp. 1124–1190, 2012. ista: Browning TD, Heath Brown R. 2012. Quadratic polynomials represented by norm forms. Geometric and Functional Analysis. 22(5), 1124–1190. mla: Browning, Timothy D., and Roger Heath Brown. “Quadratic Polynomials Represented by Norm Forms.” Geometric and Functional Analysis, vol. 22, no. 5, Springer Basel, 2012, pp. 1124–90, doi:10.1007/s00039-012-0168-5. short: T.D. Browning, R. Heath Brown, Geometric and Functional Analysis 22 (2012) 1124–1190. date_created: 2018-12-11T11:45:24Z date_published: 2012-08-25T00:00:00Z date_updated: 2021-01-12T06:57:26Z day: '25' doi: 10.1007/s00039-012-0168-5 extern: 1 intvolume: ' 22' issue: '5' month: '08' page: 1124 - 1190 publication: Geometric and Functional Analysis publication_status: published publisher: Springer Basel publist_id: '7661' quality_controlled: 0 status: public title: Quadratic polynomials represented by norm forms type: journal_article volume: 22 year: '2012' ... --- _id: '2440' abstract: - lang: eng text: We present an algorithm for computing [X, Y], i.e., all homotopy classes of continuous maps X → Y, where X, Y are topological spaces given as finite simplicial complexes, Y is (d - 1)-connected for some d ≥ 2 (for example, Y can be the d-dimensional sphere S d), and dim X ≤ 2d - 2. These conditions on X, Y guarantee that [X, Y] has a natural structure of a finitely generated Abelian group, and the algorithm finds generators and relations for it. We combine several tools and ideas from homotopy theory (such as Postnikov systems, simplicial sets, and obstruction theory) with algorithmic tools from effective algebraic topology (objects with effective homology). We hope that a further extension of the methods developed here will yield an algorithm for computing, in some cases of interest, the ℤ 2-index, which is a quantity playing a prominent role in Borsuk-Ulam style applications of topology in combinatorics and geometry, e.g., in topological lower bounds for the chromatic number of a graph. In a certain range of dimensions, deciding the embeddability of a simplicial complex into ℝ d also amounts to a ℤ 2-index computation. This is the main motivation of our work. We believe that investigating the computational complexity of questions in homotopy theory and similar areas presents a fascinating research area, and we hope that our work may help bridge the cultural gap between algebraic topology and theoretical computer science. author: - first_name: Martin full_name: Čadek, Martin last_name: Čadek - first_name: Marek full_name: Marek Krcál id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál - first_name: Jiří full_name: Matoušek, Jiří last_name: Matoušek - first_name: Francis full_name: Sergeraert, Francis last_name: Sergeraert - first_name: Lukáš full_name: Vokřínek, Lukáš last_name: Vokřínek - first_name: Uli full_name: Uli Wagner id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: 'Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing all maps into a sphere. In: SIAM; 2012:1-10.' apa: 'Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., & Wagner, U. (2012). Computing all maps into a sphere (pp. 1–10). Presented at the SODA: Symposium on Discrete Algorithms, SIAM.' chicago: Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek, and Uli Wagner. “Computing All Maps into a Sphere,” 1–10. SIAM, 2012. ieee: 'M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner, “Computing all maps into a sphere,” presented at the SODA: Symposium on Discrete Algorithms, 2012, pp. 1–10.' ista: 'Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2012. Computing all maps into a sphere. SODA: Symposium on Discrete Algorithms, 1–10.' mla: Čadek, Martin, et al. Computing All Maps into a Sphere. SIAM, 2012, pp. 1–10. short: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, in:, SIAM, 2012, pp. 1–10. conference: name: 'SODA: Symposium on Discrete Algorithms' date_created: 2018-12-11T11:57:40Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T06:57:30Z day: '01' extern: 1 main_file_link: - open_access: '0' url: http://arxiv.org/abs/1105.6257 month: '01' page: 1 - 10 publication_status: published publisher: SIAM publist_id: '4466' quality_controlled: 0 status: public title: Computing all maps into a sphere type: conference year: '2012' ...